Singular value and generalized singular value decompositions and the solution of linear matrix equations

Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators

Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD)

The singular value decomposition (SVD) is a generalization of the eigen-decomposition which can be used to analyze rectangular matrices (the eigen-decomposition is definedonly for squaredmatrices). By analogy with the eigen-decomposition, which decomposes a matrix into two simple matrices, the main idea of the SVD is to decompose a rectangular matrix into three simple matrices: Two orthogonal m...

Continuation of Singular Value Decompositions

In this work we consider computing a smooth path for a (block) singular value decomposition of a full rank matrix valued function. We give new theoretical results and then introduce and implement several algorithms to compute a smooth path. We illustrate performance of the algorithms with a few numerical examples.

Eigenvalues and Singular Values 10.1 Eigenvalue and Singular Value Decompositions

This chapter is about eigenvalues and singular values of matrices. Computational algorithms and sensitivity to perturbations are both discussed. An eigenvalue and eigenvector of a square matrix A are a scalar λ and a nonzero vector x so that Ax = λx. A singular value and pair of singular vectors of a square or rectangular matrix A are a nonnegative scalar σ and two nonzero vectors u and v so th...

Generalized Singular Value Thresholding

This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑