Volume 4, Issue 1
On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products

East Asian J. Appl. Math., 4 (2014), pp. 1-20.

Published online: 2018-02

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• Abstract

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.

• Keywords

(Weighted) Moore-Penrose inverse, weighted least squares, Kronecker product, condition number.

65F10

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@Article{EAJAM-4-1, author = {}, title = {On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {1}, pages = {1--20}, abstract = {

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.230313.070913a}, url = {http://global-sci.org/intro/article_detail/eajam/10817.html} }
TY - JOUR T1 - On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 20 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.230313.070913a UR - https://global-sci.org/intro/article_detail/eajam/10817.html KW - (Weighted) Moore-Penrose inverse, weighted least squares, Kronecker product, condition number. AB -

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.

T. T. Chen & W. Li. (1970). On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products. East Asian Journal on Applied Mathematics. 4 (1). 1-20. doi:10.4208/eajam.230313.070913a
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