An efficient parallel scheme for minimizing a sum of Euclidean norms
type: Item
instance of: scholarly article
title: An efficient parallel scheme for minimizing a sum of Euclidean norms
zbMATH Open document ID: 0677.65061
DOI: 10.1016/0024-3795(89)90692-7
author: Robert J. Plemmons
author: Stephen J. Wright
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: For the problem \(F(x)=\sum_{i}w_ i\| A_ ix-b_ i\|_ 2\to \min\), where \(w_ i>0\), \(x\in {\mathbb{R}}^ n\), \(b\in {\mathbb{R}}^{m_ i}\), \(A_ i\) \(m_ i\times n\) matrices, Newton's method with line search is developed. Using QR decompositions of the \(A_ i\) saves considerable time in evaluating \(\nabla F\), \(\nabla^ 2F\) and the line search factors. The implementation of the algorithm of an Alliant FX/8 vector multiprocessor system is described. Numerical examples are given. The computing times are so low that a vector computer seems not to be necessary at all for this type of problem.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 4109976
zbMATH Keywords: minimizing a sum of Euclidean norms
zbMATH Keywords: parallel computation
zbMATH Keywords: Newton's method
zbMATH Keywords: line search
zbMATH Keywords: QR decompositions
zbMATH Keywords: algorithm
zbMATH Keywords: vector multiprocessor system
zbMATH Keywords: Numerical examples
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90692-7
OpenAlex ID: W2031694155
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description: scientific article; zbMATH DE number 4109976