Properties of the inverse of the Gaussian matrix

The Gaussian matrix is a symmetric Toeplitz matrix and in addition the elements in its first row form a pattern. This enables a specific formula to be obtained, in the nonsingular case, for the elements in the first row of the inverse. Recurrence formulae are then obtained which enable this inverse...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 1991-07, Vol.12 (3), p.541-548
Main Author: GOVER, M. J. C
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
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Summary:The Gaussian matrix is a symmetric Toeplitz matrix and in addition the elements in its first row form a pattern. This enables a specific formula to be obtained, in the nonsingular case, for the elements in the first row of the inverse. Recurrence formulae are then obtained which enable this inverse to be obtained in $\frac{1} {2}n^2 $ flops, as against $2n^2 $ flops, for a general symmetric Toeplitz matrix using the Trench algorithm.
ISSN:0895-4798
1095-7162
DOI:10.1137/0612039