Works (4)
Updated: July 5th, 2023 15:57
2018 article
Iterative Solution of Sparse Linear Least Squares using LU Factorization
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON HIGH PERFORMANCE COMPUTING IN ASIA-PACIFIC REGION (HPC ASIA 2018), pp. 47–53.
TL;DR:
This paper explores a further preconditioning by inv(L1) where L1 is the n × n upper part of the lower trapezoidal m × n factor L, and determines whether the iteration will be effective, and whether further pre-conditioning is required.
(via Semantic Scholar)
Source: Web Of Science
Added: January 21, 2019
2016 article
LU Preconditioning for Overdetermined Sparse Least Squares Problems
PARALLEL PROCESSING AND APPLIED MATHEMATICS, PPAM 2015, PT I, Vol. 9573, pp. 128–137.
author keywords: Sparse linear least squares; Iterative methods; Preconditioning; Conjugate gradient algorithm; lsqr algorithm
TL;DR:
This work investigates how to use an LU factorization with the classical lsqr routine for solving overdetermined sparse least squares problems because usually L is much better conditioned than A and iterating with L instead of A results in faster convergence.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
2008 journal article
Cache efficient bidiagonalization using BLAS 2.5 operators
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 34(3).
author keywords: algorithms; performance; BLAS 2.5; bidiagonalization; cache-efficient; Householder reflections; matrix factorization; singular values; SVD
TL;DR:
This paper reorganizes the sequence of operations for Householder bidiagonalization of a general m × n matrix, so that two (_GEMV) vector-matrix multiplications can be done with one pass of the unreduced trailing part of the matrix through cache.
(via Semantic Scholar)
citeseerx.ist.psu.edu (repository)
Source: Web Of Science
Added: August 6, 2018
2005 journal article
Algorithm 841: BHESS: Gaussian reduction to a similar banded Hessenberg form
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 31(1), 166–185.
author keywords: algorithms; Gaussian similarity transformations; matrix eigenvalues; spectra; Hessenberg form; cache-efficient; Sylvester equation
TL;DR:
BHESS uses Gaussian similarity transformations to reduce a general real square matrix to similar upper Hessenberg form to determine a complete spectrum in about one-fifth the time required for orthogonal reduction to Hessenbergform followed by QR iterations.
(via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018
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