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On growth factors of the modified Gram–Schmidt algorithm

✍ Scribed by Musheng Wei; Qiaohua Liu

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
142 KB
Volume
15
Category
Article
ISSN
1070-5325

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✦ Synopsis

Abstract

Growth factors play a central role in studying the stability properties and roundoff estimates of matrix factorizations; therefore, they have attracted many numerical analysts to study upper bounds of these growth factors.

In this article, we derive several upper bounds of row‐wise growth factors of the modified Gram–Schmidt (MGS) algorithm to solve the least squares (LS) problem and the weighted LS problem. We also extend the analysis to the MGS‐like algorithm to solve the constrained LS problem. Copyright © 2008 John Wiley & Sons, Ltd.

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