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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Inversion of Toeplitz band matrices

Author: William F. Trench
Journal: Math. Comp. 28 (1974), 1089-1095
MSC: Primary 65F05
MathSciNet review: 0347066
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Abstract: An algorithm for inverting Toeplitz matrices is simplified for Toeplitz band matrices. In some cases, the simplification yields formulas for the elements in the first row and column of the inverse, from which the remaining elements can be easily calculated. Two examples are given. In any case, the simplification yields a recursive method for computing the first row and column of the inverse of an nth order Toeplitz band matrix with $ O(n)$ operations, where $ O({n^2})$ are required with the more general algorithm.

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Keywords: Toeplitz matrix, band matrix, inversion
Article copyright: © Copyright 1974 American Mathematical Society

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