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## Factorization
Kinds of Factorization
Terms modified by Factorization
## Selected Abstracts## A perspective factorization method for Euclidean reconstruction with uncalibrated cameras COMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 4 2002Mei HanAbstract Structure from motion (SFM), which is recovering camera motion and scene structure from image sequences, has various applications, such as scene modelling, robot navigation, object recognition and virtual reality. Most of previous research on SFM requires the use of intrinsically calibrated cameras. In this paper we describe a factorization-based method to recover Euclidean structure from multiple perspective views with uncalibrated cameras. The method first performs a projective reconstruction using a bilinear factorization algorithm, and then converts the projective solution to a Euclidean one by enforcing metric constraints. The process of updating a projective solution to a full metric one is referred as normalization in most factorization-based SFM methods. We present three normalization algorithms which enforce Euclidean constraints on camera calibration parameters to recover the scene structure and the camera calibration simultaneously, assuming zero skew cameras. The first two algorithms are linear, one for dealing with the case that only the focal lengths are unknown, and another for the case that the focal lengths and the constant principal point are unknown. The third algorithm is bilinear, dealing with the case that the focal lengths, the principal points and the aspect ratios are all unknown. The results of experiments are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Interaction of exchange and differential relaxation in the saturation recovery behavior of the binary spin-bath model for magnetization transfer CONCEPTS IN MAGNETIC RESONANCE, Issue 4 2006Gunther HelmsAbstract Most closed-form analytical solutions of the binary spin-bath are difficult to interpret in terms of underlying physics. The key notions are the presence of a kinetic and a thermal equilibrium and that the time course of saturation recovery under conditions of fast exchange can be understood as conjoint relaxation and lossless transfer. By introducing a suitable parameter, it is shown how exchange and differential relaxation counteract each other: the amount of transferred saturation (transfer term) is altered and the kinetic equilibrium appears slightly disturbed (difference term). Although the factorization formally represents the general solution of saturation recovery in the binary spin-bath, this interpretation applies only to the case of fast exchange and slow relaxation. By calculating the set of parameters for a wide range of hypothetical relaxation rates, it was shown that the difference term is crucial to describe the transition to the slow-exchange limit. The transfer term vanishes as the two pools appear decoupled in this approximation. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 291,298, 2006. [source] ## Scheduling dense linear algebra operations on multicore processors CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 1 2010Jakub KurzakAbstract State-of-the-art dense linear algebra software, such as the LAPACK and ScaLAPACK libraries, suffers performance losses on multicore processors due to their inability to fully exploit thread-level parallelism. At the same time, the coarse,grain dataflow model gains popularity as a paradigm for programming multicore architectures. This work looks at implementing classic dense linear algebra workloads, the Cholesky factorization, the QR factorization and the LU factorization, using dynamic data-driven execution. Two emerging approaches to implementing coarse,grain dataflow are examined, the model of nested parallelism, represented by the Cilk framework, and the model of parallelism expressed through an arbitrary Direct Acyclic Graph, represented by the SMP Superscalar framework. Performance and coding effort are analyzed and compared against code manually parallelized at the thread level. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Parallel tiled QR factorization for multicore architectures CONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 13 2008Alfredo ButtariAbstract As multicore systems continue to gain ground in the high-performance computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine-grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data (referred to as ,tiles'). These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. This may result in an out-of-order execution of the tasks that will completely hide the presence of intrinsically sequential tasks in the factorization. Performance comparisons are presented with the LAPACK algorithm for QR factorization where parallelism can be exploited only at the level of the BLAS operations and with vendor implementations. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## PCA- and PMF-based methodology for air pollution sources identification and apportionment ENVIRONMETRICS, Issue 8 2009Marie ChaventAbstract Air pollution is a wide concern for human health and requires the development of air quality control strategies. In order to achieve this goal pollution sources have to be accurately identified and quantified. The case study presented in this paper is part of a scientific project initiated by the French Ministry of Ecology and Sustainable Development. For the following study measurements of chemical composition data for particles have been conducted on a French urban site. The first step of the study consists in the identification of the sources profiles which is achieved through principal component analysis (PCA) completed by a rotation technique. Then the apportionment of the sources is evaluated with a receptor modeling using positive matrix factorization (PMF) as estimation method. Finally the joint use of these two statistical methods enables to characterize and apportion five different sources of fine particulate emission. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Paraxial ray methods for anisotropic inhomogeneous media GEOPHYSICAL PROSPECTING, Issue 1 2007Tijmen Jan MoserABSTRACT A new formalism of surface-to-surface paraxial matrices allows a very general and flexible formulation of the paraxial ray theory, equally valid in anisotropic and isotropic inhomogeneous layered media. The formalism is based on conventional dynamic ray tracing in Cartesian coordinates along a reference ray. At any user-selected pair of points of the reference ray, a pair of surfaces may be defined. These surfaces may be arbitrarily curved and oriented, and may represent structural interfaces, data recording surfaces, or merely formal surfaces. A newly obtained factorization of the interface propagator matrix allows to transform the conventional 6 × 6 propagator matrix in Cartesian coordinates into a 6 × 6 surface-to-surface paraxial matrix. This matrix defines the transformation of paraxial ray quantities from one surface to another. The redundant non-eikonal and ray-tangent solutions of the dynamic ray-tracing system in Cartesian coordinates can be easily eliminated from the 6 × 6 surface-to-surface paraxial matrix, and it can be reduced to 4 × 4 form. Both the 6 × 6 and 4 × 4 surface-to-surface paraxial matrices satisfy useful properties, particularly the symplecticity. In their 4 × 4 reduced form, they can be used to solve important boundary-value problems of a four-parametric system of paraxial rays, connecting the two surfaces, similarly as the well-known surface-to-surface matrices in isotropic media in ray-centred coordinates. Applications of such boundary-value problems include the two-point eikonal, relative geometrical spreading, Fresnel zones, the design of migration operators, and more. [source] ## Eigensolution of symmetric frames using graph factorization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2004A. KavehAbstract In this paper, decomposition of matrices of special patterns to submatrices of smaller dimensions is briefly described. The graph models of frame structures with different symmetries are decomposed and appropriate processes are designed for their healing in order to form the corresponding factors. The eigenvalues and eigenvectors of the entire structure are then obtained by evaluating those of its factors. The methods developed in this article, simplifies the calculation of the natural frequencies and natural modes of the planar frames with different types of symmetry. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## A priori pivoting in solving the Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002S. Ø. WilleAbstract Mixed finite element formulations of incompressible Navier,Stokes Equations leads to non-positive definite algebraic systems inappropriate for iterative solution techniques. However, introducing a suitable preconditioner, the mixed finite element equation system becomes positive definite and solvable by iterative techniques. The present work suggests a priori pivoting sequences for parallel and serial implementations of incomplete Gaussian factorization. Tests are performed for the driven cavity problem in two and three dimensions. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009J. K. ReidAbstract In many applications where the efficient solution of large sparse linear systems of equations is required, a direct method is frequently the method of choice. Unfortunately, direct methods have a potentially severe limitation: as the problem size grows, the memory needed generally increases rapidly. However, the in-core memory requirements can be limited by storing the matrix and its factors externally, allowing the solver to be used for very large problems. We have designed a new out-of-core package for the large sparse unsymmetric systems that arise from finite-element problems. The code, which is called HSL_MA78, implements a multifrontal algorithm and achieves efficiency through the use of specially designed code for handling the input/output operations and efficient dense linear algebra kernels. These kernels, which are available as a separate package called HSL_MA74, use high-level BLAS to perform the partial factorization of the frontal matrices and offer both threshold partial and rook pivoting. In this paper, we describe the design of HSL_MA78 and explain its user interface and the options it offers. We also describe the algorithms used by HSL_MA74 and illustrate the performance of our new codes using problems from a range of practical applications. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Construction of shape functions for the h - and p -versions of the FEM using tensorial product INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007M. L. BittencourtAbstract This paper presents an uniform and unified approach to construct h - and p -shape functions for quadrilaterals, triangles, hexahedral and tetrahedral based on the tensorial product of one-dimensional Lagrange and Jacobi polynomials. The approach uses indices to denote the one-dimensional polynomials in each tensorization direction. The appropriate manipulation of the indices allows to obtain hierarchical or non-hierarchical and inter-element C0 continuous or non-continuous bases. For the one-dimensional elements, quadrilaterals, triangles and hexahedral, the optimal weights of the Jacobi polynomials are determined, the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated. A brief discussion of the use of sum factorization and computational implementation is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A preconditioned conjugate gradient approach to structural reanalysis for general layout modifications INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007Zhengguang LiAbstract This paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications. It is suitable for all types of layout modifications, including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently. The approach is based on the preconditioned conjugate gradient technique. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that the condition number of the preconditioned matrix is remarkably reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Peter ArbenzAbstract The goal of our paper is to compare a number of algorithms for computing a large number of eigenvectors of the generalized symmetric eigenvalue problem arising from a modal analysis of elastic structures. The shift-invert Lanczos algorithm has emerged as the workhorse for the solution of this generalized eigenvalue problem; however, a sparse direct factorization is required for the resulting set of linear equations. Instead, our paper considers the use of preconditioned iterative methods. We present a brief review of available preconditioned eigensolvers followed by a numerical comparison on three problems using a scalable algebraic multigrid (AMG) preconditioner. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## On singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems with corners INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004A. DimitrovAbstract In this paper, a numerical procedure is presented for the computation of corner singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems near corners of various shape. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of this problem is approximated using a mixed u, p Galerkin,Petrov finite element method. Additionally, a separation of variables is used to reduce the dimension of the original problem. As a result, the quadratic eigenvalue problem (P+,Q+,2R)d=0 is obtained, where the saddle-point-type matrices P, Q, R are defined explicitly. For a numerical solution of the algebraic eigenvalue problem an iterative technique based on the Arnoldi method in combination with an Uzawa-like scheme is used. This technique needs only one direct matrix factorization as well as few matrix,vector products for finding all eigenvalues in the interval ,,(,) , (,0.5, 1.0), as well as the corresponding eigenvectors. Some benchmark tests show that this technique is robust and very accurate. Problems from practical importance are also analysed, for instance the surface-breaking crack in an incompressible elastic material and the three-dimensional viscous flow of a Newtonian fluid past a trihedral corner. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## A class of parallel multiple-front algorithms on subdomains INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003A. BoseAbstract A class of parallel multiple-front solution algorithms is developed for solving linear systems arising from discretization of boundary value problems and evolution problems. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill-conditioning may occur due to differing material properties or the use of high degree finite elements (p methods). Next, the method is implemented on distributed-memory multiprocessor systems with the final reduced (small) Schur complement problem solved on a single processor. A novel algorithm that implements a recursive partitioning approach on the subdomain interfaces is then developed. Both algorithms are implemented and compared in a least-squares finite-element scheme for viscous incompressible flow computation using h - and p -finite element schemes. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Physics-based preconditioner for iterative algorithms in multi-scatterer and multi-boundary method of moments formulations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Jürgen v. HagenAbstract An efficient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. So far, the method of moments has successfully been applied to large arrays of identical scatterers when it was combined with preconditioned iterative algorithms to solve for the linear system of equations. Here, the method is generalized to geometries that are composed of several metallic elements of different shapes and sizes, and also to scatterers that are composed of metallic and dielectric regions. The method uses in its core an iterative algorithm, preferably the transpose-free quasi-minimum residual (TFQMR) algorithm, and a block diagonal Jacobi preconditioner. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers for the array case, and according to the electric and magnetic current basis functions for dielectric/metallic scatterers. The iterative procedure converges quickly for an optimally chosen preconditioner, and is robust even for a non-optimal preconditioner. Reported run times are compared to run times of an efficiently programmed LU factorization, and are shown to be significantly lower. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Efficient computation of order and mode of corner singularities in 3D-elasticity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2001A. DimitrovAbstract A general numerical procedure is presented for the efficient computation of corner singularities, which appear in the case of non-smooth domains in three-dimensional linear elasticity. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of the problem is approximated by a Galerkin,Petrov finite element method. A quadratic eigenvalue problem (P+,Q+,2R) u=0 is obtained, with explicitly analytically defined matrices P,Q,R. Moreover, the three matrices are found to have optimal structure, so that P,R are symmetric and Q is skew symmetric, which can serve as an advantage in the following solution process. On this foundation a powerful iterative solution technique based on the Arnoldi method is submitted. For not too large systems this technique needs only one direct factorization of the banded matrix P for finding all eigenvalues in the interval ,e(,),(,0.5,1.0) (no eigenpairs can be ,lost') as well as the corresponding eigenvectors, which is a great improvement in comparison with the normally used determinant method. For large systems a variant of the algorithm with an incomplete factorization of P is implemented to avoid the appearance of too much fill-in. To illustrate the effectiveness of the present method several new numerical results are presented. In general, they show the dependence of the singular exponent on different geometrical parameters and the material properties. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5-6 2001K. MocellinAbstract The industrial simulation code Forge3® is devoted to three-dimensional metal forming applications. This finite element software is based on an implicit approach. It is able to carry out the large deformations of viscoplastic incompressible materials with unilateral contact conditions. The finite element discretization is based on a stable mixed velocity,pressure formulation and tetrahedral unstructured meshes. Central to the Newton iterations dealing with the non-linearities, a preconditioned conjugate residual method (PCR) is used. The parallel version of the code uses an SPMD programming model and several results on complex applications have been published. In order to reduce the CPU time computation, a new solver has been developed which is based on multigrid theory. A detailed presentation of the different elements of the method is given: the geometrical approach based on embedded meshes, the direct resolution of the velocity,pressure system, the use of PCR method as an original smoother and for solving the coarse problem, the full multigrid method and the required preconditioning by an incomplete Cholesky factorization for problems with complex contact conditions. By considering different forging cases, the theoretical properties of the multigrid method are numerically verified, optimizations of the solver are presented and finally, the results obtained on several industrial problems are given, showing the efficiency of the new solver that provides speed-up larger than 5. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## A hybrid Padé ADI scheme of higher-order for convection,diffusion problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2010Samir KaraaArticle first published online: 8 SEP 200Abstract A high-order Padé alternating direction implicit (ADI) scheme is proposed for solving unsteady convection,diffusion problems. The scheme employs standard high-order Padé approximations for spatial first and second derivatives in the convection-diffusion equation. Linear multistep (LM) methods combined with the approximate factorization introduced by Beam and Warming (J. Comput. Phys. 1976; 22: 87,110) are applied for the time integration. The approximate factorization imposes a second-order temporal accuracy limitation on the ADI scheme independent of the accuracy of the LM method chosen for the time integration. To achieve a higher-order temporal accuracy, we introduce a correction term that reduces the splitting error. The resulting scheme is carried out by repeatedly solving a series of pentadiagonal linear systems producing a computationally cost effective solver. The effects of the approximate factorization and the correction term on the stability of the scheme are examined. A modified wave number analysis is performed to examine the dispersive and dissipative properties of the scheme. In contrast to the HOC-based schemes in which the phase and amplitude characteristics of a solution are altered by the variation of cell Reynolds number, the present scheme retains the characteristics of the modified wave numbers for spatial derivatives regardless of the magnitude of cell Reynolds number. The superiority of the proposed scheme compared with other high-order ADI schemes for solving unsteady convection-diffusion problems is discussed. A comparison of different time discretizations based on LM methods is given. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Lyapunov spectrum determination from the FEM simulation of a chaotic advecting flow INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006Philippe CarrièreArticle first published online: 7 SEP 200Abstract The problem of the determination of the Lyapunov spectrum in chaotic advection using approximated velocity fields resulting from a standard FEM method is investigated. A fourth order Runge,Kutta scheme for trajectory integration is combined with a third order Jacobian matrix method with QR -factorization. After checking the algorithm on the standard Lorenz and coupled quartic oscillator systems, the method is applied to a model 3-D steady flow for which an analytical expression is known. Both linear and quadratic approximated velocity fields succeed in predicting the Lyapunov exponents as well as describing the chaotic or regular regions inside the flow with satisfactory accuracy. A more realistic flow is then studied in order to delineate the possible limitations of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## An implicit velocity decoupling procedure for the incompressible Navier,Stokes equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002Kyoungyoun KimAbstract An efficient numerical method to solve the unsteady incompressible Navier,Stokes equations is developed. A fully implicit time advancement is employed to avoid the Courant,Friedrichs,Lewy restriction, where the Crank,Nicolson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity,pressure decoupling is achieved in conjunction with the approximate factorization. The main emphasis is placed on the additional decoupling of the intermediate velocity components with only nth time step velocity. The temporal second-order accuracy is preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving several test cases, in particular, the turbulent minimal channel flow unit. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Asynchronous orthogonal decision-feedback multiuser detector (AODFD) and its alternative decoding strategies INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 6 2001Hsiao-Hwa ChenAbstract This paper proposes a new CDMA multiuser detector, asynchronous orthogonal decision-feedback detector (AODFD), and its alternative decoding schemes. The proposed AODFD does not require an infinitely long whiten filter in its feed-forward stage, however, which is necessary in the traditional ADDFD detector reported in the literature. The updating algorithm of the AODFD detector is also much simplified if compared with that of ADDFD that requires computational intensive z -transformed matrix inversion and spectral factorization. Results show that, despite its low complexity, the AODFD performs very well under multiple access interference. The proposed two new decoding strategies can also be chosen to cater for different operating scenarios. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Efficient computation for the noisy MAX INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2003Francisco J. DíezDíez's algorithm for the noisy MAX is very efficient for polytrees, but when the network has loops, it has to be combined with local conditioning, a suboptimal propagation algorithm. Other algorithms, based on several factorizations of the conditional probability of the noisy MAX, are not as efficient for polytrees but can be combined with general propagation algorithms such as clustering or variable elimination, which are more efficient for networks with loops. In this article we propose a new factorization of the noisy MAX that amounts to Díez's algorithm in the case of polytrees and at the same time is more efficient than previous factorizations when combined with either variable elimination or clustering. © 2003 Wiley Periodicals, Inc. [source] ## Development of 3-D equivalent-circuit modelling with decoupled L-ILU factorization in semiconductor-device simulation INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2007Szu-Ju LiAbstract In this paper, we develop a three-dimensional (3-D) device simulator, which combines a simplified, decoupled Gummel-like method equivalent-circuit model (DM) with levelized incomplete LU (L-ILU) factorization. These complementary techniques are successfully combined to yield an efficient and robust method for semiconductor-device simulation. The memory requirements are reduced significantly compared to the conventionally used Newton-like method. Furthermore, the complex voltage-controlled current source (VCCS) is simplified as a nonlinear resistor. Hence, the programming and debugging for the nonlinear resistor model is much easier than that for the VCCS model. Further, we create a connection-table to arrange the scattered non-zero fill-ins in sparse matrix to increase the efficiency of L-ILU factorization. Low memory requirements may pave the way for the widespread application in 3-D semiconductor-device simulation. We use the body-tied silicon-on-insulator MOSFET structure to illustrate the capability and the efficiency of the 3-D DM equivalent-circuit model with L-ILU factorization. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Symplectic molecular dynamics integration using normal mode analysis INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2001anka JaneAbstract The split integration symplectic method (SISM) for molecular dynamics (MD) integration using normal mode analysis based on a factorization of the Liouville propagator is presented. This approach is quite distinct from others that use fractional-step methods, owing to the analytical treatment of high-frequency motions. The method involves splitting the total Hamiltonian of the system into a harmonic part and the remaining part. Then the Hamilton equations are solved using a second-order generalized leapfrog integration scheme in which the purely harmonic Hamiltonian (which represents the main contribution of the chemical bonds and angles) is treated analytically, i.e., independent of the step size of integration, by a normal mode analysis that is carried out only once, at the beginning of calculation. The whole integration step combines analytical evolution of the harmonic part of the Hamiltonian with a correction arising from the remaining part. The proposed algorithm requires only one force evaluation per integration step. The algorithm was tested on a simple system of linear chain molecules. Results demonstrate the method makes possible the integration of the MD equations over larger time steps without loss of stability while being economical in computer time. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 84: 2,12, 2001 [source] ## Stable robust feedback control system design for unstable plants with input constraints using robust right coprime factorization INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2007Mingcong DengAbstract A stable robust control system design problem for unstable plants with input constraints is considered using robust right coprime factorization of nonlinear operator. For obtaining strong stability of the closed-loop system of unstable plants with input constraints, a design scheme of robust nonhyphen-linear control system is given based on robust right coprime factorization. Some conditions for the robustness and system output tracking of the unstable plant with input constraints are derived. Numerical examples are given to demonstrate the validity of the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Multi-component analysis: blind extraction of pure components mass spectra using sparse component analysis JOURNAL OF MASS SPECTROMETRY (INCORP BIOLOGICAL MASS SPECTROMETRY), Issue 9 2009Ivica KoprivaAbstract The paper presents sparse component analysis (SCA)-based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on ,1 norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Factorized approach to nonlinear MPC using a radial basis function model AICHE JOURNAL, Issue 2 2001Sharad BhartiyaA new computationally efficient approach for nonlinear model predictive control (NMPC) presented here uses the factorability of radial basis function (RBF) process models in a traditional model predictive control (MPC) framework. The key to the approach is to formulate the RBF process model that can make nonlinear predictions across a p-step horizon without using future unknown process measurements. The RBF model avoids error propagation from use of model predictions us input in a recursive or iterative manner. The resulting NMPC formulation using the RBF model provides analytic expressions for the gradient and Hessian of the controller's objective function in terms of RBF network parameters. Solution of the NMPC optimization problem is simplifed significantly by factorization of the RBF model output into terms containing only known and unknown parts of the process. [source] ## A Wiener,Hopf approximation technique for a multiple plate diffraction problem MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2004James R. BrannanAbstract An approximation method is derived for the computation of the acoustic field between a series of parallel plates, subject to a time periodic incident field. The method is based on the Wiener,Hopf method of factorization, with computations involving orthogonal bases of functions that are analytic in the complex half-plane. Copyright 2004 John Wiley & Sons, Ltd. [source] ## Generalized factorization for N×N Daniele,Khrapkov matrix functions MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2001M. C. CâmaraAbstract A generalization to N×N of the 2×2 Daniele,Khrapkov class of matrix-valued functions is proposed. This class retains some of the features of the 2×2 Daniele,Khrapkov class, in particular, the presence of certain square-root functions in its definition. Functions of this class appear in the study of finite-dimensional integrable systems. The paper concentrates on giving the main properties of the class, using them to outline a method for the study of the Wiener,Hopf factorization of the symbols of this class. This is done through examples that are completely worked out. One of these examples corresponds to a particular case of the motion of a symmetric rigid body with a fixed point (Lagrange top). Copyright © 2001 John Wiley & Sons, Ltd. [source] ## On factorization of Schatten class type mappings MATHEMATISCHE NACHRICHTEN, Issue 9-10 2006Cristiane de Andrade MendesAbstract We present some results on factorization of multilinear mappings and polynomials of Schatten class type ,,2 through infinite dimensional Banach spaces, ,1 and ,, spaces. We conclude this work with a factorization result for holomorphic mappings of Schatten class type ,,2. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] |