scholarly journals On the partial condition numbers for the indefinite least squares problem

2018 ◽  
Vol 123 ◽  
pp. 200-220 ◽  
Author(s):  
Hanyu Li ◽  
Shaoxin Wang
Keyword(s):  
Least Squares ◽  
Condition Numbers ◽  
Least Squares Problem ◽  
Partial Condition

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.

scholarly journals On the Condition Number Theory of the Equality Constrained Indefinite Least Squares Problem

2018 ◽  
Vol 34 ◽  
pp. 619-638
Author(s):  
Shaoxin Wang ◽  
Hanyu Li ◽  
Hu Yang
Keyword(s):  
Number Theory ◽  
Least Squares ◽  
Condition Number ◽  
Condition Numbers ◽  
Least Squares Problems ◽  
Unified Framework ◽  
Least Squares Problem ◽  
Practical Applications ◽  
New Findings ◽  
Special Cases

In this paper, within a unified framework of the condition number theory, the explicit expression of the \emph{projected} condition number of the equality constrained indefinite least squares problem is presented. By setting specific norms and parameters, some widely used condition numbers, like the normwise, mixed and componentwise condition numbers follow as its special cases. Considering practical applications and computation, some new compact forms or upper bounds of the projected condition numbers are given to improve the computational efficiency. The new compact forms are of particular interest in calculating the exact value of the 2-norm projected condition numbers. When the equality constrained indefinite least squares problem degenerates into some specific least squares problems, our results give some new findings on the condition number theory of these specific least squares problems. Numerical experiments are given to illustrate our theoretical results.

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