scholarly journals PRECONDITIONED PARALLEL BLOCK–JACOBI SVD ALGORITHM

2006 ◽  
Vol 16 (03) ◽  
pp. 371-379 ◽  
Author(s):  
GABRIEL OKŠA ◽  
MARIÁN VAJTERŠIC
Keyword(s):  
Execution Time ◽  
Parallel Architecture ◽  
Singular Values ◽  
Singular Value ◽  
Parallel Execution ◽  
Qr Factorization ◽  
R Factor ◽  
Order Of Magnitude ◽  
Column Pivoting ◽  
Parallel Iteration

We show experimentally, that the QR factorization with the complete column pivoting, optionally followed by the LQ factorization of the R-factor, can lead to a substantial decrease of the number of outer parallel iteration steps in the parallel block-Jacobi SVD algorithm, whereby the details depend on the condition number and on the shape of spectrum, including the multiplicity of singular values. Best results were achieved for well-conditioned matrices with a multiple minimal singular value, where the number of parallel iteration steps has been reduced by two orders of magnitude. However, the gain in speed, as measured by the total parallel execution time, depends decisively on how efficient is the implementation of the distributed QR and LQ factorizations on a given parallel architecture. In general, the reduction of the total parallel execution time up to one order of magnitude has been achieved.

New Dynamic Orderings for the Parallel One–Sided Block-Jacobi SVD Algorithm

2015 ◽  
Vol 25 (02) ◽  
pp. 1550003 ◽  
Author(s):  
Martin Bečka ◽  
Gabriel Okša ◽  
Marián Vajteršic
Keyword(s):  
Random Distribution ◽  
Singular Values ◽  
Parallel Execution ◽  
Jacobi Method ◽  
Stopping Criteria ◽  
The Matrix ◽  
Blocking Factors ◽  
Relative Errors ◽  
Parallel Iteration ◽  
Global And Local

Five variants of a new dynamic ordering are presented for the parallel one-sided block Jacobi SVD algorithm. Similarly to the two-sided algorithm, the dynamic ordering takes into account the actual status of a matrix—this time of its block columns with respect to their mutual orthogonality. Variants differ in the computational and communication complexities and in proposed global and local stopping criteria. Their performance is tested on a square random matrix of order 8192 with a random distribution of singular values using [Formula: see text], 32, 64, 96 and 128 processors. All variants of dynamic ordering are compared with a parallel cyclic ordering, two-sided block-Jacobi method with dynamic ordering and the ScaLAPACK routine PDGESVD with respect to the number of parallel iteration steps needed for the convergence and total parallel execution time. Moreover, the relative errors in the orthogonality of computed left singular vectors and in the matrix assembled from computed singular triplets are also discussed. It turns out that the variant 3, for which a local optimality in some precisely defined sense can be proved, and its combination with variant 2, are the most efficient ones. For relatively small blocking factors [Formula: see text], they outperform the ScaLAPACK procedure PDGESVD and are about 2 times faster.

scholarly journals Cache Servers Placement Based on Important Switches for SDN-Based ICN

Electronics ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 39 ◽  
Author(s):  
Jan Badshah ◽  
Majed Mohaia Alhaisoni ◽  
Nadir Shah ◽  
Muhammad Kamran
Keyword(s):  
Energy Consumption ◽  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Optimization Problem ◽  
Computation Time ◽  
Singular Value ◽  
Qr Factorization ◽  
Traffic Matrix ◽  
Column Pivoting ◽  
Value Decomposition

In centralized cache management for SDN-based ICN, it is an optimization problem to compute the location of cache servers and takes a longer time. We solve this problem by proposing to use singular-value-decomposition (SVD) and QR-factorization with column pivoting methods of linear algebra as follows. The traffic matrix of the network is lower-rank. Therefore, we compute the most important switches in the network by using SVD and QR-factorization with column pivoting methods. By using real network traces, the results show that our proposed approach reduces the computation time significantly, and also decreases the traffic overhead and energy consumption as compared to the existing approach.

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

scholarly journals Householder QR Factorization With Randomization for Column Pivoting (HQRRP)

2017 ◽  
Vol 39 (2) ◽  
pp. C96-C115 ◽  
Author(s):  
Per-Gunnar Martinsson ◽  
Gregorio Quintana OrtÍ ◽  
Nathan Heavner ◽  
Robert van de Geijn
Keyword(s):  
Qr Factorization ◽  
Column Pivoting

scholarly journals Through-Wall Image Enhancement Based on Singular Value Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Mohsin Riaz ◽  
Abdul Ghafoor
Keyword(s):  
Singular Value Decomposition ◽  
Image Enhancement ◽  
Visual Inspection ◽  
Signal To Noise Ratio ◽  
Singular Values ◽  
Singular Value ◽  
Information Theoretic ◽  
Value Decomposition ◽  
Suppress Noise ◽  
Wall Imaging

Singular value decomposition and information theoretic criterion-based image enhancement is proposed for through-wall imaging. The scheme is capable of discriminating target, clutter, and noise subspaces. Information theoretic criterion is used with conventional singular value decomposition to find number of target singular values. Furthermore, wavelet transform-based denoising is performed (to further suppress noise signals) by estimating noise variance. Proposed scheme works also for extracting multiple targets in heavy cluttered through-wall images. Simulation results are compared on the basis of mean square error, peak signal to noise ratio, and visual inspection.

scholarly journals LARGE INFORMATION PLUS NOISE RANDOM MATRIX MODELS AND CONSISTENT SUBSPACE ESTIMATION IN LARGE SENSOR NETWORKS

2012 ◽  
Vol 01 (02) ◽  
pp. 1150006 ◽  
Author(s):  
WALID HACHEM ◽  
PHILIPPE LOUBATON ◽  
XAVIER MESTRE ◽  
JAMAL NAJIM ◽  
PASCAL VALLET
Keyword(s):  
Covariance Matrix ◽  
Estimation Method ◽  
Singular Values ◽  
Subspace Methods ◽  
Localization Function ◽  
Random Matrix Models ◽  
Order Of Magnitude ◽  
Source Signal ◽  
Subspace Estimation ◽  
Empirical Covariance

In array processing, a common problem is to estimate the angles of arrival of K deterministic sources impinging on an array of M antennas, from N observations of the source signal, corrupted by Gaussian noise. In the so-called subspace methods, the problem reduces to estimate a quadratic form (called "localization function") of a certain projection matrix related to the source signal empirical covariance matrix. The estimates of the angles of arrival are then obtained by taking the K deepest local minima of the estimated localization function. Recently, a new subspace estimation method has been proposed, in the context where the number of available samples N is of the same order of magnitude than the number of sensors M. In this context, the traditional subspace methods tend to fail because they are based on the empirical covariance matrix of the observations which is a poor estimate of the source signal covariance matrix. The new subspace method is based on a consistent estimator of the localization function in the regime where M and N tend to +∞ at the same rate. However, the consistency of the angles estimator was not addressed, and the purpose of this paper is to prove this consistency in the previous asymptotic regime. For this, we prove the property that the singular values of M × N Gaussian information plus noise matrix escape from certain intervals is an event of probability decreasing at rate [Formula: see text] for all p. A regularization trick is also introduced, which allows to confine these singular values into certain intervals and to use standard tools as Poincaré inequality to characterize any moments of the estimator. These results are believed to be of independent interest.

Lyapunov and marginal instability in Hamiltonian systems

1999 ◽  
Vol 77 (8) ◽  
pp. 603-633 ◽  
Author(s):  
J Grindlay
Keyword(s):  
Lyapunov Exponents ◽  
Nonlinear Oscillator ◽  
Linear Chain ◽  
Mathieu Equation ◽  
Singular Values ◽  
Space Velocity ◽  
Singular Value ◽  
The Stability ◽  
Value Decomposition ◽  
Simple Systems

The variational equations and the evolution matrix are introduced and used to discuss the stability of a bound Hamiltonian trajectory. Singular-value decomposition is applied to the evolution matrix. Singular values and Lyapunov exponents are defined and their properties described. The singular-value expansion of the phase-space velocity is derived. Singular values and Lyapunov exponents are used to characterize the stability behaviour of five simple systems, namely, the nonlinear oscillator with cubic anharmonicity, the quasi-periodic Mathieu equation, the Hénon-Heilesmodel, the 4+2 linear chain with cubic anharmonicity, and an integrable system of arbitrary order.PACS Nos.: 03.20, 05.20

scholarly journals Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification

2019 ◽  
Vol 22 (12) ◽  
pp. 2687-2698 ◽  
Author(s):  
Zhen Chen ◽  
Lifeng Qin ◽  
Shunbo Zhao ◽  
Tommy HT Chan ◽  
Andy Nguyen
Keyword(s):  
Singular Value Decomposition ◽  
Singular Values ◽  
Singular Value ◽  
Decomposition Algorithm ◽  
Identification Accuracy ◽  
Piecewise Polynomial ◽  
Truncated Singular Value Decomposition ◽  
Force Identification ◽  
Moving Force ◽  
Value Decomposition

This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decomposition algorithm extracts the useful responses from truncated small singular values and superposes it into the solution of truncated singular value decomposition, which can be useful in moving force identification. In this article, a comprehensive numerical simulation is set up to evaluate piecewise polynomial truncated singular value decomposition, and compare this technique against truncated singular value decomposition and singular value decomposition. Numerically simulated data are processed to validate the novel method, which show that regularization matrix [Formula: see text] and truncating point [Formula: see text] are the two most important governing factors affecting identification accuracy and ill-posedness immunity of piecewise polynomial truncated singular value decomposition.

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