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- W2073943554 abstract "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 $Ax = b$." @default.
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- W2073943554 date "1986-01-01" @default.
- W2073943554 modified "2023-10-07" @default.
- W2073943554 title "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix" @default.
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- W2073943554 doi "https://doi.org/10.1137/0907011" @default.
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