Open AccessCondition numbers of the least squares problems with multiple right-hand sides
Author(s) -
Lingsheng Meng,
Bing Zheng
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1906667m
Subject(s) - mathematics , combinatorics , least squares function approximation , rank (graph theory) , condition number , matrix (chemical analysis) , linear least squares , statistics , linear model , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , estimator , composite material
In this paper, we investigate the normwise, mixed and componentwise condition numbers of the least squares problem min X?Rnxd ||X - B||F, where A ? Rmxn is a rank-deficient matrix and B ? Rmxd. The closed formulas or upper bounds for these condition numbers are presented, which extend the earlier work for the least squares problem with single right-hand side (i.e. B ? b is an m-vector) of several authors. Numerical experiments are given to confirm our results.