ON THE CHOICE OF SIGN DEFINING HOUSEHOLDER TRANSFORMATIONS

被引：0

作者：

Overton, Michael l. ^{[1
]}

Yu, Pinze ^{[1
]}

机构：

[1] NYU, New York, NY 10012 USA

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2025年 / 15卷 / 02期

基金：

美国国家科学基金会;

关键词：

Householder transformation; QR factorization; numerical stability; cancellation; choice of sign;

D O I：

10.3934/naco.2023025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancel-lation and hence numerical instability. In this note we point out that when the "wrong" choice of sign is used, the extent of the resulting instability depends in a somewhat subtle way on the data leading to cancellation.

引用

页码：502 / 505

页数：4

共 7 条

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[6] Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations
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[7] Solving of Eigenvalue and Singular Value Problems via Modified Householder Transformations on Shared Memory Parallel Computing Systems
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