计算三对角矩阵条件数的新算法

本文通过数值计算例子说明了Ｈｉｇｈａｍ提出的部分算法的数值稳定性是值得探讨的，并了三对角矩阵条件数的计算。基于矩阵的三角分解提出两个计算对角占优型三对角矩阵条件数‖Ａ‖∞的新方法，理论结果和实例计算表明该算法是数值稳定的，最后给出了一个计算一般三角矩阵条件数的方法和数值实例。

The New Algorithms for Computing the Condition Number of Tridiagonal Matrix

In this paper, the numerical stability of partial algorithms presented by Higham is discussed by the examples of numerical calculation, and the calculation for condition number of tridiagonal matrix is also discussed. Based on the trianguler decomposition of the matrix, two new methods for compating the condition numcer of a tridiagonal matrix are presented. The results in theory and practical calculation show that the methods are numerical stable. As to the general tridiagonal matrix, a method and some numerical examples are given.