CONDITION NUMBER FOR WEIGHTED LINEAR LEAST SQUARES PROBLEM

• 来源期刊: 计算数学（英文版）
• 关键词: Moore-Penrose inverse.Condition number.Linear least squares
• 年，卷（期）: 2007,（5）
• 页码范围: 561-572
• 页数: 12页
• 语种: 英文

摘要

In this paper,we investigate the condition numbers for the generalized matrix inversion and the rank deficient linear least squares problem:minx ||Ax-b||2,where A is an m-by-n (m≥n)rank deficient matrix.We first derive an explicit expression for the condition number in the weighted Frobenius norm || [AT,βb]||F of the data A and b,where T is a positive diagonal matrix and β is a positive scalar.We then discuss the sensitivity of the standard 2-norm condition numbers for the generalized matrix inversion and rank deficient least squares and establish relations between the condition numbers and their condition numbers called level-2 condition numbers.