Efficient algorithms for computing the condition number of a tridagonal matrix
Efficient algorithms for computing the condition number of a tridagonal matrix
复制标题
计算三角矩阵条件数的高效算法
DOI：
10.1137/0907011
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
N. Higham
中科院分区：
文献类型：
--
作者：
N. Higham
Let A be a tridiagonal matrix of order n. We show that it is possible to compute ${\|A^{ - 1} \|}_\infty $,and hence $\operatorname{cond}_\infty (A)$, in $O(n)$ operations. Several algorithms which perform this task are given and their numerical properties are investigated.If A is also positive definite then ${\|A^{ - 1} \|}_\infty $ can be computed as the norm of the solution to a positive definite tridiagonal linear system whose coefficient matrix is closely related to A. We show how this computation can be carried out in parallel with the solution of a linear system $Ax = b$. In particular we describe some simple modifications to the LINPACK routine SPTSL which enable this routine to compute $\operatorname{cond}_1 (A)$, efficiently, in addition to solving $Ax = b$.
