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Matrix Inversion (matrix + inversion)
Selected AbstractsA Rosenbrock-W method for real-time dynamic substructuring and pseudo-dynamic testingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2009C. P. Lamarche Abstract A variant of the Rosenbrock-W integration method is proposed for real-time dynamic substructuring and pseudo-dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Spectral estimation on a sphere in geophysics and cosmologyGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2008F. A. Dahlen SUMMARY We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the one-dimensional (1-D) periodogram, (ii) the maximum-likelihood method and (iii) a spherical analogue of the 1-D multitaper method. The periodogram exhibits strong spectral leakage, especially for small regions of area A, 4,, and is generally unsuitable for spherical spectral analysis applications, just as it is in 1-D. The maximum-likelihood method is particularly useful in the case of nearly-whole-sphere coverage, A, 4,, and has been widely used in cosmology to estimate the spectrum of the cosmic microwave background radiation from spacecraft observations. The spherical multitaper method affords easy control over the fundamental trade-off between spectral resolution and variance, and is easily implemented regardless of the region size, requiring neither non-linear iteration nor large-scale matrix inversion. As a result, the method is ideally suited for most applications in geophysics, geodesy or planetary science, where the objective is to obtain a spatially localized estimate of the spectrum of a signal from noisy data within a pre-selected and typically small region. [source] Hybrid finite compact-WENO schemes for shock calculationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Yiqing Shen Abstract Hybrid finite compact (FC)-WENO schemes are proposed for shock calculations. The two sub-schemes (finite compact difference scheme and WENO scheme) are hybridized by means of the similar treatment as in ENO schemes. The hybrid schemes have the advantages of FC and WENO schemes. One is that they possess the merit of the finite compact difference scheme, which requires only bi-diagonal matrix inversion and can apply the known high-resolution flux to obtain high-performance numerical flux function; another is that they have the high-resolution property of WENO scheme for shock capturing. The numerical results show that FC-WENO schemes have better resolution properties than both FC-ENO schemes and WENO schemes. In addition, some comparisons of FC-ENO and artificial compression method (ACM) filter scheme of Yee et al. are also given. Copyright © 2006 John Wiley & Sons, Ltd. [source] A novel approach to enable decorrelating multiuser detection without matrix inversion operationsINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 9 2004Hsiao-Hwa Chen Abstract This paper proposes a non-matrix inversion based algorithm to implement decorrelating detection (DD), namely quasi-decorrelating detector (QDD), which uses truncated matrix series expansion to overcome the problems associated with the matrix inversion in DD, such as noise enhancement, computational complexity and matrix singularity, etc. Two alternative QDD implementation schemes are presented in this paper; one is to use multi-stage feedforward filters and the other is to use an nth order single matrix filter (neither of which involves matrix inversion). In addition to significantly reduced computational complexity if compared with DD, the QDD algorithm offers a unique flexibility to trade among MAI suppression, near-far resistance and noise enhancement depending on varying system set-ups. The obtained results show that the QDD outperforms DD in either AWGN or multipath channel if a proper number of feed-forward stages can be used. We will also study the impact of correlation statistics of spreading codes on the QDD's performance with the help of a performance-determining factor derived in the paper, which offers a code-selection guideline for the optimal performance of QDD algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Adaptive joint beamforming and B-MMSE detection for CDMA signal reception under multipath interferenceINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 7 2004Hsiao-Hwa Chen Abstract The combination of antenna array beamforming with multiuser detection can effectively improve the detection efficiency of a wireless system under multipath interference, especially in a fast-fading channel. This paper studies the performance of an adaptive beamformer incorporated with a block-wise minimum mean square error(B-MMSE) detector, which works on a unique signal frame characterized by training sequence preamble and data blocks segmented by zero-bits. Both beam-former weights updating and B-MMSE detection are carried out by either least mean square (LMS) or recursive least square (RLS) algorithm. The comparison of the two adaptive algorithms applied to both beamformer and B-MMSE detector will be made in terms of convergence behaviour and estimation mean square error. Various multipath patterns are considered to test the receiver's responding rapidity to changing multipath interference. The performance of the adaptive B-MMSE detector is also compared with that of non-adaptive version (i.e. through direct matrix inversion). The final performance in error probability simulation reveals that the RLS/B-MMSE scheme outperforms non-adaptive B-MMSE by 1,5 dB, depending on the multipath channel delay profiles of concern. The obtained results also suggest that adaptive beamformer should use RLS algorithm for its fast and robust convergence property; while the B-MMSE filter can choose either LMS or RLS algorithm depending on antenna array size, multipath severity and implementation complexity. Copyright © 2004 John Wiley & Sons, Ltd. [source] Asynchronous orthogonal decision-feedback multiuser detector (AODFD) and its alternative decoding strategiesINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 6 2001Hsiao-Hwa Chen Abstract 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] Atomic resolution crystal structure of squid ganglion DFPaseACTA CRYSTALLOGRAPHICA SECTION D, Issue 10-1 2002Juergen Koepke Diisopropylfluorophosphatases (DFP-ases) are capable of detoxifying chemical warfare agents like diisopropylfluorophosphate (DFP) by hydrolysis. The protein reported here was recombinantely expressed in E. coli. The X-ray cystal structure of this enzyme has been refined to a resolution of 0.85 Å and a crystallographic R value of 9.4%. Reversible flash-cooling improved both, mosaicity and resolution of the crystals considerably. The overall structure of this protein represents a six-bladed ,-propeller with two calcium ions bound in a central water filled tunnel. 496 water, 2 glycerol, 2 MES-buffer molecules, and 18 PEG fragments of different lengths could be refined in the solvent region. The 208 most reliable residues, without disorder or reduced occupancy in their side-chains, were finally refined without restraints. A subsequent full-matrix refinement cycle for the positional parameters yielded estimated standard deviations (esds) by matrix inversion. The herewith calculated bond lenghts and bond-esds were used to obtain averaged bond lengths, which have been compared to the restraints used in preceding refinement cycles. [source] Evaluating products of matrix pencils and collapsing matrix productsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6-7 2001Peter Benner Abstract This paper describes three numerical methods to collapse a formal product of p pairs of matrices down to the product of a single pair Ê,1Â. In the setting of linear relations, the product formally extends to the case in which some of the Ek's are singular and it is impossible to explicitly form P as a single matrix. The methods differ in flop count, work space, and inherent parallelism. They have in common that they are immune to overflows and use no matrix inversions. A rounding error analysis shows that the special case of collapsing two pairs is numerically backward stable. Copyright © 2001 John Wiley & Sons, Ltd. [source] Hierarchical Spatial Modeling of Additive and Dominance Genetic Variance for Large Spatial Trial DatasetsBIOMETRICS, Issue 2 2009Andrew O. Finley Summary This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein,Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability. [source] | |||||||||||||