نتایج جستجو برای: singular matrix

تعداد نتایج: 411825  

1999
Benedikt Grosser

We present a parallel software implementation for computing the singular value decomposition (SVD) of general, banded or bidiagonal matrices. First, the matrix is reduced to bidiagonal form. This reduction can be rearranged in a way that allows heavy use of matrix-matrix operations. Then the singular values are computed in an iterative process. Finally the singular vectors are computed independ...

Journal: :Computers & Mathematics with Applications 2008
Emedin Montaño Mario Salas Ricardo L. Soto

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n−1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n×n nonnegative bidiagonal matrix B and an n×n nonnegative semi-bordered diagonal matrix C , such that σ ( j) 1 and σ ( j) j are, respectively, the minimal and the maximal singular values of certai...

2002
Michiel Hochstenbach

The computation (or approximation) of some of the smallest or largest singular values of a large sparse matrix is a big challenge, having many important applications. In this talk we discuss approximations to singular triples that can be obtained from subspaces. One of the topics is the concept of harmonic singular triples, introduced in [1]. The word “harmonic” expresses the fact that we try t...

2008
S. J. Sangwine N. Le Bihan

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

Journal: :CoRR 2017
Ratnik Gandhi Amoli Rajgor

An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems. It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a Cauchy matrix-vector product. With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank1 perturbed ma...

Journal: :Advances in Mathematics: Scientific Journal 2020

Journal: :Linear Algebra and its Applications 1984

Journal: :Journal of Mathematical Inequalities 2022

In this article, we show multiple inequalities for the singular values of difference matrix means. The obtained results refine and complement some well established in literature. Although target inequalities, will several means as well.

1999
D. P. OLEARY G. W. STEWART

In this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. Instead of computing eigenvector approximations by the inverse power method, we take them to be the singular vecto...

Journal: :Journal of Pure and Applied Algebra 1992

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