Volume 10, Issue 4
Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis

East Asian J. Appl. Math., 10 (2020), pp. 679-697.

Published online: 2020-08

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• Abstract

Block updating and downdating algorithms for regularised least squares problems with multiple right-hand sides based on the economical $QR$ decomposition are proposed. They exploit the initial coefficient matrix structure and use existing solution to establish a solution of the amended problem. Such an approach demonstrates its efficiency in terms of the memory required and the computational cost. Applications to linear discriminant analysis are considered and numerical experiments involving realworld databases show the efficiency of the methods.

• Keywords

Block updating, block downdating, regularised least squares problem, economical QR decomposition, linear discriminant analysis.

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@Article{EAJAM-10-679, author = {Wei Wei , and Hua Dai , and Weitai Liang , }, title = {Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {679--697}, abstract = {

Block updating and downdating algorithms for regularised least squares problems with multiple right-hand sides based on the economical $QR$ decomposition are proposed. They exploit the initial coefficient matrix structure and use existing solution to establish a solution of the amended problem. Such an approach demonstrates its efficiency in terms of the memory required and the computational cost. Applications to linear discriminant analysis are considered and numerical experiments involving realworld databases show the efficiency of the methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.171219.220220 }, url = {http://global-sci.org/intro/article_detail/eajam/17946.html} }
TY - JOUR T1 - Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis AU - Wei Wei , AU - Hua Dai , AU - Weitai Liang , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 679 EP - 697 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.171219.220220 UR - https://global-sci.org/intro/article_detail/eajam/17946.html KW - Block updating, block downdating, regularised least squares problem, economical QR decomposition, linear discriminant analysis. AB -

Block updating and downdating algorithms for regularised least squares problems with multiple right-hand sides based on the economical $QR$ decomposition are proposed. They exploit the initial coefficient matrix structure and use existing solution to establish a solution of the amended problem. Such an approach demonstrates its efficiency in terms of the memory required and the computational cost. Applications to linear discriminant analysis are considered and numerical experiments involving realworld databases show the efficiency of the methods.

Wei Wei, Hua Dai & Weitai Liang. (2020). Block Updating/Downdating Algorithms for Regularised Least Squares Problems and Applications to Linear Discriminant Analysis. East Asian Journal on Applied Mathematics. 10 (4). 679-697. doi:10.4208/eajam.171219.220220
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