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## Subspaces
Terms modified by Subspaces
## Selected Abstracts## Face recognition based on face-specific subspace INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2003Shiguang ShanAbstract In this article, we present an individual appearance model based method, named face-specific subspace (FSS), for recognizing human faces under variation in lighting, expression, and viewpoint. This method derives from the traditional Eigenface but differs from it in essence. In Eigenface, each face image is represented as a point in a low-dimensional face subspace shared by all faces; however, the experiments conducted show one of the demerits of such a strategy: it fails to accurately represent the most discriminanting features of a specific face. Therefore, we propose to model each face with one individual face subspace, named Face-Specific Subspace. Distance from the face-specific subspace, that is, the reconstruction error, is then exploited as the similarity measurement for identification. Furthermore, to enable the proposed approach to solve the single example problem, a technique to derive multisamples from one single example is further developed. Extensive experiments on several academic databases show that our method significantly outperforms Eigenface and template matching, which intensively indicates its robustness under variation in illumination, expression, and viewpoint. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13: 23,32, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10047 [source] ## MATLAB based GUIs for linear controller design via convex optimization COMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2003Wathanyoo KhaisongkramAbstract Owing to the current evolution of computational tools, a complicated parameter optimization problem could be effectively solved by a computer. In this paper, a CAD tool for multi-objective controller design based on MATLAB program is developed. In addition, we construct simple GUIs (using GUIDE tools within MATLAB) to provide a visual approach in specifying the constraints. The linear controller design problem can be cast as the convex optimization subjected to time domain and frequency domain constraints. This optimization problem is efficiently solved within a finite dimensional subspace by a practical ellipsoid algorithm. In the design process, we include a model reduction of the resulting controller to speed up the computational efficiency. Finally, a numerical example shows the capability of the program to design multi-objective controller for a one-link flexible robot arm. © 2003 Wiley Periodicals, Inc. Comput Appl Eng Educ 11: 13,24, 2003; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.10035 [source] ## Fast and Efficient Skinning of Animated Meshes COMPUTER GRAPHICS FORUM, Issue 2 2010L. KavanAbstract Skinning is a simple yet popular deformation technique combining compact storage with efficient hardware accelerated rendering. While skinned meshes (such as virtual characters) are traditionally created by artists, previous work proposes algorithms to construct skinning automatically from a given vertex animation. However, these methods typically perform well only for a certain class of input sequences and often require long pre-processing times. We present an algorithm based on iterative coordinate descent optimization which handles arbitrary animations and produces more accurate approximations than previous techniques, while using only standard linear skinning without any modifications or extensions. To overcome the computational complexity associated with the iterative optimization, we work in a suitable linear subspace (obtained by quick approximate dimensionality reduction) and take advantage of the typically very sparse vertex weights. As a result, our method requires about one or two orders of magnitude less pre-processing time than previous methods. [source] ## A reduced-order modeling technique for tall buildings with active tuned mass damper EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2001Zu-Qing QuAbstract It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reduced-order control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reduced-order system is updated repeatedly until a desired one is obtained, the accuracy of the reduced-order system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. Another advantage of the method is that the reduced-order system is defined in the subspace of the original physical space, which makes the state vectors have physical meaning. An eigenvalue shifting technique is applied to accelerate the convergence of iteration and to make the reduced system retain all the dynamic characteristics of the full system within a given frequency range. Two schemes to establish the reduced-order system by using the proposed method are also presented and discussed in this paper. The results for a tall building with active tuned mass damper show that the proposed method is efficient for the reduced-order modelling and the accuracy is very close to exact only after two iterations. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Accelerating iterative solution methods using reduced-order models as solution predictors INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006R. MarkovinoviAbstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Application of model-free LQG subspace predictive control to TCP congestion control INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2008Belinda A. ChieraAbstract We investigate the application of a model-free linear quadratic Gaussian (LQG) subspace-based predictive controller to Internet congestion control. Specifically, we consider a classically designed LQG linear congestion controller with a non-standard performance index and determine whether a model-free controller is a viable alternative in this instance. We employ the model-free subspace predictive controller methodology which we customize for end-to-end transmission control protocol (TCP) congestion control. A series of network simulations support the use of the more easily implementable model-free controller over its classical analogue. We further demonstrate that the model-free controller provides increased stability under transient network conditions when compared with the first feedback congestion controller, TCP Vegas. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Real-time identification of vehicle chassis dynamics using a novel reparameterization based on sensitivity invariance INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2004S. BrennanAbstract This work presents a novel methodology to identify model parameters using the concept of sensitivity invariance. Within many classical system representations, relationships between Bode parameter sensitivities may exist that are not explicitly accounted for by the formal system model. These relationships, called sensitivity invariances, will explicitly limit the possible parameter variation of the system model to a small subspace of the possible parameter gradients. By constraining the parameter identification or adaptation to a model structure with uncoupled parameter sensitivities, a more efficient identification can be obtained at a reduced computational and modelling cost. As illustration, an identification method of using sensitivity invariance is demonstrated on an experimental problem to identify, in real time, a time-varying tire parameter associated with the chassis dynamics of passenger vehicles at highway speeds. The results are validated with simulations as well as an experimental implementation on a research vehicle driven under changing road conditions. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Face recognition based on face-specific subspace INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2003Shiguang ShanAbstract In this article, we present an individual appearance model based method, named face-specific subspace (FSS), for recognizing human faces under variation in lighting, expression, and viewpoint. This method derives from the traditional Eigenface but differs from it in essence. In Eigenface, each face image is represented as a point in a low-dimensional face subspace shared by all faces; however, the experiments conducted show one of the demerits of such a strategy: it fails to accurately represent the most discriminanting features of a specific face. Therefore, we propose to model each face with one individual face subspace, named Face-Specific Subspace. Distance from the face-specific subspace, that is, the reconstruction error, is then exploited as the similarity measurement for identification. Furthermore, to enable the proposed approach to solve the single example problem, a technique to derive multisamples from one single example is further developed. Extensive experiments on several academic databases show that our method significantly outperforms Eigenface and template matching, which intensively indicates its robustness under variation in illumination, expression, and viewpoint. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13: 23,32, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10047 [source] ## Application of Krylov subspaces to SPECT imaging INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2002P. CalviniThe application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two-dimensional case) to 15 (three-dimensional case). On this basis, a new, proposed approach can be basically summarized as follows: construction of a basis spanning a Krylov subspace of suitable dimension and projection of the projector,backprojector matrix (a 106 × 106 matrix in the three-dimensional case) onto such a subspace. In this way, one is led to a problem of low dimensionality, for which regularized solutions can be easily and quickly obtained. The required SPECT activity map is expanded as a linear combination of the basis elements spanning the Krylov subspace and the regularization acts by modifying the coefficients of such an expansion. By means of a suitable graphical interface, the tuning of the regularization parameter(s) can be performed interactively on the basis of the visual inspection of one or some slices cut from a reconstruction. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 217,228, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10026 [source] ## Krylov model order reduction of finite element approximations of electromagnetic devices with frequency-dependent material properties INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2007Hong WuAbstract A methodology is presented for the Krylov subspace-based model order reduction of finite element models of electromagnetic structures with material properties and impedance boundary conditions exhibiting arbitrary frequency dependence. The proposed methodology is a generalization of an equation-preserving Krylov model order reduction scheme for methodology for second-order, linear dynamical systems. The emphasis of this paper is on the application of this method to the broadband model order reduction of planar circuits including lossy strips of arbitrary thickness and lossy reference planes. In particular, it is shown that the proposed model order reduction methodology provides for the accurately modelling of the impact of the frequency dependence of the internal impedance per unit length of the thick lossy strip on the electromagnetic response of the stripline structure over a very broad, multi-GHz frequency band, extending all the way down to frequencies in the DC neighbourhood. In addition, the application of the proposed methodology to the broadband modelling of electromagnetic coupling between strips on either side of a lossy ground plane is demonstrated. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Construction of switching sequences for reachability realization of switched impulsive control systems INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2008Zhijian JiAbstract This paper studies the construction of switching sequences for reachability realization of switched impulsive control systems. An approach is proposed to design switching sequences so that the reachable subspace of switched impulsive control systems is expressed in terms of the reachable state sets of the designed switching sequences. For a class of switched impulsive control systems, it is proved that a single switching sequence can be designed with its reachable state set coinciding with the reachable subspace. Periodic switching sequences are also constructed in this paper for the reachability realization problem. The results present a new way to exploit the switching mechanism to achieve the reachability and controllability of switched impulsive control systems. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Robust multiple-fault detection filter INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2002Robert H. ChenAbstract A new robust multiple-fault detection and identification algorithm is determined. Different from other algorithms which explicitly force the geometric structure by using eigenstructure assignment or geometric theory, this algorithm is derived from solving an optimization problem. The output error is divided into several subspaces. For each subspace, the transmission from one fault, denoted the associated target fault, is maximized while the transmission from other faults, denoted the associated nuisance fault, is minimized. Therefore, each projected residual of the robust multiple-fault detection filter is affected primarily by one fault and minimally by other faults. The transmission from process and sensor noises is also minimized so that the filter is robust with respect to these disturbances. It is shown that, in the limit where the weighting on each associated nuisance fault transmission goes to infinity, the filter recovers the geometric structure of the restricted diagonal detection filter of which the Beard,Jones detection filter and unknown input observer are special cases. Filter designs can be obtained for both time-invariant and time-varying systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## The Role of Charge Localization in Current-Driven Dynamics ISRAEL JOURNAL OF CHEMISTRY, Issue 1 2007Ryan JornWe explore the role of charge localization in current-triggered, resonance-mediated, dynamical events in molecular junctions. To that end we use a simple model for a molecular rattle, a Li+C9H,9 zwitterion attached between two metal clusters. By varying the size of the metal clusters we systematically vary the degree of delocalization of the electronic orbitals underlying the resonant current, and thus can draw general conclusions regarding the effect of delocalization on dynamical processes induced by resonance inelastic current in molecular electronics. In the small cluster limit, we find interesting quantum dynamics in the nuclear subspace, corresponding to coherent tunneling of the wave packet through the barrier of an asymmetric double-well potential. These dynamics are rapidly damped with increasing charge delocalization in extended systems. [source] ## A diagonal measure and a local distance matrix to display relations between objects and variables, JOURNAL OF CHEMOMETRICS, Issue 1 2010Gergely TóthAbstract Proper permutation of data matrix rows and columns may result in plots showing striking information on the objects and variables under investigation. To control the permutation first, a diagonal matrix measureD was defined expressing the size relations of the matrix elements. D is essentially the absolute norm of a matrix where the matrix elements are weighted by their distance to the matrix diagonal. Changing the order of rows and columns increases or decreases D. Monte Carlo technique was used to achieve maximum D in the case of the object distance matrix or even minimal D in the case of the variable correlation matrix to get similar objects or variables close together. Secondly, a local distance matrix was defined, where an element reflects the distances of neighboring objects in a limited subspace of the variables. Due to the maximization of D in the local distance matrix by row and column changes of the original data matrix, the similar objects were arranged close to each other and simultaneously the variables responsible for their similarity were collected close to the diagonal part defined by these objects. This combination of the diagonal measure and the local distance matrix seems to be an efficient tool in the exploration of hidden similarities of a data matrix. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2010Halvor S. HansenAbstract A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit-solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of ,- D -glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build-up protocol, even for relatively short build-up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010 [source] ## A robust calibration modeling strategy for analysis of interference-subject spectral data AICHE JOURNAL, Issue 1 2010Chunhui ZhaoAbstract Preprocessing and correction of mixture spectra have been an important issue with regard to the removal of undesired systematic variation due to variations in environmental, instrumental, or sample conditions. In this article, a new robust calibration modeling strategy is proposed on the basis of independent component analysis (ICA). It aims at separating the interference-subject parasitic subspace from the interference-immune common subspace among all considered cases. The common subspace is further divided into two orthogonal parts according to their relationship with quality: one is quality-irrelevant and the other is quality-informative, in which, only the second part is employed for quality prediction. Focusing on each subspace, it identifies distinct types of underlying source components underlying different spectra subspaces, analyzes their characteristics and roles, and accordingly models them for different applications, respectively. This approach provides a comprehensive insight into the inherent nature of interference-subject mixture spectra. Furthermore, several model statistics are defined to give quantitative indication on the effectiveness of the correction strategy. The feasibility and performance of the proposed method are illustrated with data from laboratory experiments. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] ## Invariant co-ordinate selection JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2009David E. TylerSummary., A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue,eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given. [source] ## Dimension reduction for the conditional kth moment in regression JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2002Xiangrong YinThe idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the central kth-moment subspace to capture information from the mean, variance and so on up to the kth conditional moment of the regression. New methods are studied for estimating these subspaces. Connections with sliced inverse regression are established, and examples illustrating the theory are presented. [source] ## On a formula for the spectral flow and its applications MATHEMATISCHE NACHRICHTEN, Issue 5 2010Pierluigi BenevieriAbstract We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Infinitesimal deformations of double covers of smooth algebraic varieties MATHEMATISCHE NACHRICHTEN, Issue 7 2006awomir CynkAbstract The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi,Yau threefolds which are non-singular models of double cover of the projective 3-space branched along an octic surface. We show that in that case the number of deformations can be computed explicitly using computer algebra systems. This gives a method to compute the Hodge numbers of these Calabi,Yau manifolds. In this case the transverse deformations are resolutions of deformations of double covers of projective space but not double covers of a blow-up of projective space. In the paper we gave many explicit examples. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Computing a partial generalized real Schur form using the Jacobi,Davidson method NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2007Tycho van NoordenAbstract In this paper, a new variant of the Jacobi,Davidson (JD) method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugate pair of eigenvalues, the method computes the two-dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. Both real and complex formulations of the correction equation are considered. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Linear system solution by null-space approximation and projection (SNAP) NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2007M. IliAbstract Solutions of large sparse linear systems of equations are usually obtained iteratively by constructing a smaller dimensional subspace such as a Krylov subspace. The convergence of these methods is sometimes hampered by the presence of small eigenvalues, in which case, some form of deflation can help improve convergence. The method presented in this paper enables the solution to be approximated by focusing the attention directly on the ,small' eigenspace (,singular vector' space). It is based on embedding the solution of the linear system within the eigenvalue problem (singular value problem) in order to facilitate the direct use of methods such as implicitly restarted Arnoldi or Jacobi,Davidson for the linear system solution. The proposed method, called ,solution by null-space approximation and projection' (SNAP), differs from other similar approaches in that it converts the non-homogeneous system into a homogeneous one by constructing an annihilator of the right-hand side. The solution then lies in the null space of the resulting matrix. We examine the construction of a sequence of approximate null spaces using a Jacobi,Davidson style singular value decomposition method, called restarted SNAP-JD, from which an approximate solution can be obtained. Relevant theory is discussed and the method is illustrated by numerical examples where SNAP is compared with both GMRES and GMRES-IR. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Convergence conditions for a restarted GMRES method augmented with eigenspaces NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2005Jan ZítkoArticle first published online: 9 AUG 200Abstract We consider the GMRES(m,k) method for the solution of linear systems Ax=b, i.e. the restarted GMRES with restart m where to the standard Krylov subspace of dimension m the other subspace of dimension k is added, resulting in an augmented Krylov subspace. This additional subspace approximates usually an A -invariant subspace. The eigenspaces associated with the eigenvalues closest to zero are commonly used, as those are thought to hinder convergence the most. The behaviour of residual bounds is described for various situations which can arise during the GMRES(m,k) process. The obtained estimates for the norm of the residual vector suggest sufficient conditions for convergence of GMRES(m,k) and illustrate that these augmentation techniques can remove stagnation of GMRES(m) in many cases. All estimates are independent of the choice of an initial approximation. Conclusions and remarks assessing numerically the quality of proposed bounds conclude the paper. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Krylov subspaces and the analytic grade NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2005M. IliAbstract Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Lanczos, Householder transformations, and implicit deflation for fast and reliable dominant singular subspace computation NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2001Ricardo D. FierroAbstract Many applications, such as subspace-based models in information retrieval and signal processing, require the computation of singular subspaces associated with the k dominant, or largest, singular values of an m×n data matrix A, where k,min(m,n). Frequently, A is sparse or structured, which usually means matrix,vector multiplications involving A and its transpose can be done with much less than ,,(mn) flops, and A and its transpose can be stored with much less than ,,(mn) storage locations. Many Lanczos-based algorithms have been proposed through the years because the underlying Lanczos method only accesses A and its transpose through matrix,vector multiplications. We implement a new algorithm, called KSVD, in the Matlab environment for computing approximations to the singular subspaces associated with the k dominant singular values of a real or complex matrix A. KSVD is based upon the Lanczos tridiagonalization method, the WY representation for storing products of Householder transformations, implicit deflation, and the QR factorization. Our Matlab simulations suggest it is a fast and reliable strategy for handling troublesome singular-value spectra. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 647 2010Anna TrevisanAbstract Key apriori information used in 4D-Var is the knowledge of the system's evolution equations. In this article we propose a method for taking full advantage of the knowledge of the system's dynamical instabilities in order to improve the quality of the analysis. We present an algorithm for four-dimensional variational assimilation in the unstable subspace (4D-Var , AUS), which consists of confining in this subspace the increment of the control variable. The existence of an optimal subspace dimension for this confinement is hypothesized. Theoretical arguments in favour of the present approach are supported by numerical experiments in a simple perfect nonlinear model scenario. It is found that the RMS analysis error is a function of the dimension N of the subspace where the analysis is confined and is a minimum for N approximately equal to the dimension of the unstable and neutral manifold. For all assimilation windows, from 1 to 5 d, 4D-Var , AUS performs better than standard 4D-Var. In the presence of observational noise, the 4D-Var solution, while being closer to the observations, is farther away from the truth. The implementation of 4D-Var , AUS does not require the adjoint integration. Copyright © 2010 Royal Meteorological Society [source] ## Computational relaxed TP model transformation: restricting the computation to subspaces of the dynamic model, ASIAN JOURNAL OF CONTROL, Issue 5 2009Szabolcs NagyAbstract The tensor-product (TP) model transformation is a recently proposed numerical method capable of transforming linear parameter varying state-space models to the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. It is also capable of generating various types of convex TP models, a type of polytop models, for linear matrix inequality based controller design. The crucial point of the TP model transformation is that its computational load exponentially explodes with the dimensionality of the parameter vector of the parameter-varying state-space model. In this paper we propose a modified TP model transformation that leads to considerable reduction of the computation. The key idea of the method is that instead of transforming the whole system matrix at once in the whole parameter space, we decompose the problem and perform the transformation element wise and restrict the computation to the subspace where the given element of the model varies. The modified TP model transformation can readily be executed in higher dimensional cases when the original TP model transformation fails. The effectiveness of the new method is illustrated with numerical examples. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] ## Adaptive Control For Robotic Manipulators Executing Multilateral Constrained Task ASIAN JOURNAL OF CONTROL, Issue 1 2003Haruhisa KawasakiABSTRACT This paper presents a model-based adaptive control in task coordinates for robotic manipulators executing multilateral constrained tasks The controller works based on the concept of orthogonality between force and motion in the subspaces derived from the constraints. The control gains are independently adjustable in each subspace. The friction force, depending on the contact force, is compensated adaptively. Asymptotic convergence for both force and motion tracking errors is guaranteed by the Lyapunov-Like Lemma. Experimental results obtained using a 3 D.O.F. robot are given. [source] ## Real-space protein-model completion: an inverse-kinematics approach ACTA CRYSTALLOGRAPHICA SECTION D, Issue 1 2005Henry Van Den BedemRapid protein-structure determination relies greatly on software that can automatically build a protein model into an experimental electron-density map. In favorable circumstances, various software systems are capable of building over 90% of the final model. However, completeness falls off rapidly with the resolution of the diffraction data. Manual completion of these partial models is usually feasible, but is time-consuming and prone to subjective interpretation. Except for the N- and C-termini of the chain, the end points of each missing fragment are known from the initial model. Hence, fitting fragments reduces to an inverse-kinematics problem. A method has been developed that combines fast inverse-kinematics algorithms with a real-space torsion-angle refinement procedure in a two-stage approach to fit missing main-chain fragments into the electron density between two anchor points. The first stage samples a large number of closing conformations, guided by the electron density. These candidates are ranked according to density fit. In a subsequent refinement stage, optimization steps are projected onto a carefully chosen subspace of conformation space to preserve rigid geometry and closure. Experimental results show that fitted fragments are in excellent agreement with the final refined structure for lengths of up to 12,15 residues in areas of weak or ambiguous electron density, even at medium to low resolution. [source] ## DETECTING INFLUENTIAL OBSERVATIONS IN SLICED INVERSE REGRESSION ANALYSIS AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2006Luke A. PrendergastSummary The detection of influential observations on the estimation of the dimension reduction subspace returned by Sliced Inverse Regression (SIR) is considered. Although there are many measures to detect influential observations in related methods such as multiple linear regression, there has been little development in this area with respect to dimension reduction. One particular influence measure for a version of SIR is examined and it is shown, via simulation and example, how this may be used to detect influential observations in practice. [source] |