2.奇异值分解(Singular Value Decomposition) 与特征值问题有关系的一个主题是奇异值分解。在某种意义上,它是特征值问题对任意矩阵的推广. A为复数域上的m×n 的矩阵,则A有可能分解为如下形式 (4)A=UΣV† 其中U∈Um,V∈U(n), Σ 是m×n 对角元为非负实数的矩阵,这些对角元称为奇异值(singular v...
Singular value decompositionOne-sided Jacobi methodReduced SVDOrthogonal matricesPerturbationsIll-conditioningWell conditionedCyclic-by-row methodHanowa matrixThis chapter develops two algorithms for the computation of the SVD. The first of these is the one-sided Jacobi method. By properly choosing c and ...
The chapter presents the Demmel and Kahan zero-shift QR downward sweep algorithm that transforms the upper-bidiagonal matrix to a diagonal matrix of singular values using bulge chasing. 展开 关键词: SVD Singular value decomposition One-sided Jacobi method Reduced SVD Orthogonal matrices Perturbations ...
We analyze when it is possible to compute the singular values and singular vectors of a matrix with high relative accuracy. This means that each computed singular value is guaranteed to have some correct digits, even if the singular values have widely varying magnitudes. This is in contrast to...
摘要原文 article Free Access Share on An Improved Algorithm for Computing the Singular Value Decomposition Author: Tony F. Chan Department of Computer Science, Yale University, 10 Hillhouse Avenue, P.O. Box, 2158 Yale Station, New Haven, CT Department of Computer Science, Yale University, 10 ...
Z. Bai, Note on the quadratic convergence of Kogbetliantz algorithm for computing the singular value decomposition, Lin. Alg. Appl., 104:131{140(1988).Z. Bai, Note on the quadratic convergence of Kogbetliantz's algorithm for computing the sin- gular value decomposition, Linear Algebra and...
A singular value thresholding algorithm for matrix completion SIAM J Optim, 20 (4) (2010), pp. 1956-1982 Google Scholar Cited by (1) A hybrid algorithm for computing a partial singular value decomposition satisfying a given threshold 2024, Numerical Algorithms©...
In this paper, we study the computation of the singular value decomposition of a matrix on the ILLIAC IV computer. We describe the architecture of the machine and explain why the standard Golub-Reinsch algorithm is not applicable to this problem. We then present a one-sided orthogonalization me...
Singular value decomposition on GPU using CUDA Linear algebra algorithms are fundamental to many computing applications. Modern GPUs are suited for many general purpose processing tasks and have emerged... S Lahabar,PJ Narayanan - IEEE International Symposium on Parallel & Distributed Processing 被引量...
singular value decomposition (SVDA new algorithm for computing the approximate GCD of multivariate polynomials is proposed by modifying the PC-PRS algorithm for exact GCD. We have implemented the new algorithm and compared it by typical examples with (approximate) PRS, (approximate) EZ-GCD ...