杨玲玲,李寒宇.带多重右边的不定最小二乘问题的条件数[J].数学研究及应用,2017,37(6):725~742
带多重右边的不定最小二乘问题的条件数
Condition Numbers for Indefinite Least Squares Problem with Multiple Right-Hand Sides
投稿时间:2016-11-15  最后修改时间:2017-02-27
DOI:10.3770/j.issn:2095-2651.2017.06.008
中文关键词:  不定最小二乘问题  多重右边  范数型条件数  混合型条件数  分量型条件数  结构条件数.
英文关键词:indefinite least squares problem  multiple right-hand sides  normwise condition number  mixed condition number  componentwise condition number  structured condition number
基金项目:国家自然科学基金 (Grant No.11671060), 中央高校基本科研业务费专项资金 (Grant No.106112015CDJXY100003).
作者单位
杨玲玲 重庆大学数学与统计学院, 重庆 401331 
李寒宇 重庆大学数学与统计学院, 重庆 401331 
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中文摘要:
      本文研究了带多重右边的不定最小二乘问题的条件数,给出了范数型、混合型及分量型条件数的表达式,同时,也给出了相应的结构条件数的表达式.所考虑的结构矩阵包含Toeplitz 矩阵、Hankel矩阵、对称矩阵、三对角矩阵等线性结构矩阵与Vandermonde矩阵、Cauchy矩阵等非线性结构矩阵.数值例子显示结构条件数总是紧于非结构条件数.
英文摘要:
      In this paper, we investigate the condition numbers for indefinite least squares problem with multiple right-hand sides. The normwise, mixed and componentwise condition numbers and the corresponding structured condition numbers are presented. The structured matrices under consideration include the linear structured matrices, such as the Toeplitz, Hankel, symmetric, and tridiagonal matrices, and the nonlinear structured matrices, such as the Vandermonde and Cauchy matrices. Numerical examples show that the structured condition numbers are tighter than the unstructured ones.
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