LSP Matrix Decomposition Revisited
نویسنده
چکیده
In this paper, we study the problem of computing an LSP-decomposition of a matrix over a field. This decomposition is an extension to arbitrary matrices of the well-known LUP-decomposition of full rowrank matrices. We present three different ways of computing an LSPdecomposition, that are both rank-sensitive and based on matrix multiplication. In each case, for an m by n input matrix of unknown rank r, the cost we obtain is in O(mnrω−2) for ω > 2. When r is small, this improves the O(nmω−1) complexity bound of Ibarra, Moran and Hui.
منابع مشابه
The inverse problem of nonsymmetric matrices with a submatrix constraint and its approximation
In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r , find a matrix A ∈ Rn×n such that ‖XTAX − B‖ = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n× n matrix à with Ã([1, r])...
متن کاملTraining a Linear Neural Network with a Stable Lsp Solution for Jamming Cancellation
Two jamming cancellation algorithms are developed based on a stable solution of least squares problem (LSP) provided by regularization. They are based on filtered singular value decomposition (SVD) and modifications of the Greville formula. Both algorithms allow an efficient hardware implementation. Testing results on artificial data modeling difficult real-world situations are also provided
متن کاملComments on "A Simple and Accurate Algorithm for Barycentric Rational Interpolation"
First, I would like to thank the author of ”Comments on ’A Simple and Accurate Algorithm for Barycentric Rational Interpolation’” (hereafter referred to as ”the comments”) for their interest in my work [1]. The author of the comments points out a novel relationship between barycentric rational interpolation, the Welch-Berlekamp key equation and Gröbner bases. This could turn out to be a very pr...
متن کاملBlind Image Deblurring Using Row-Column Sparse Representations
Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recover the deblurred image. The problem is of strong practical relevance since many imaging devices such as cellphone cameras, must rely on deblurring algorithms to yield satisfactory image quality. Despite significant research effort, handling large motions r...
متن کاملRank-profile revealing Gaussian elimination and the CUP matrix decomposition
Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the well known variations of such decompositions and transformations that have been proposed in the literature. We present an algorithm to compute the CUP decompos...
متن کامل