scholarly journals Normwise condition numbers of the indefinite least squares problem with multiple right-hand sides

2021 ◽  
Vol 7 (3) ◽  
pp. 3692-3700
Author(s):  
Limin Li ◽  
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Upper Bounds ◽  
Condition Numbers ◽  
Frobenius Norm ◽  
Least Squares Problem ◽  
Right Hand ◽  
Weighted Frobenius Norm

<abstract><p>In this paper, we investigate the normwise condition numbers of the indefinite least squares problem with multiple right-hand sides with respect to the weighted Frobenius norm and $ 2 $-norm. The closed formulas or upper bounds for these condition numbers are presented, which extend the earlier work for the indefinite least squares problem with single right-hand side. Numerical experiments are performed to illustrate the tightness of the upper bounds.</p></abstract>

scholarly journals Condition numbers of the least squares problems with multiple right-hand sides

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1667-1676
Author(s):  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Upper Bounds ◽  
Condition Numbers ◽  
Least Squares Problems ◽  
Least Squares Problem ◽  
Right Hand

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.

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