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The Hadamard product of two Brownian matrices: Analytic inverse and determinant

Published online by Cambridge University Press:  17 February 2009

F. N. Valvi
F. N. Valvi
Affiliation:
Department of Mathematics, University of Patras, Patras, Greece.
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Abstract

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The explicit inverse and determinant of a class of matrices is given. The class is the Hadamard product of two already known classes. Its elements are defined by 3n − 1 parameters, analytical expressions of which compose the Hessenberg form inverse. These expressions enable a recursive formula to be obtained, which gives the inverse in O(n2) multiplications/divisions and O(n) additions/subtractions.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 4 , April 1995 , pp. 493 - 497
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Carayannis, G., Kalouptsidis, N. and Manolakis, D. G., “Fast recursive algorithms for a class of linear equations”, IEEE Trans. Acoust. Speech Signal Process. 30 (1982) 227–239.CrossRefGoogle Scholar
[2]Frank, W. L., “Computing eigenvalues of complex matrices by determinant evaluation and by methods of Danilewski and Wielandt”, SIAM J. 6 (1958) 378–392.Google Scholar
[3]Gover, M. J. C. and Barnett, S., “Brownian matrices: properties and extensions”, Internat. J. Systems Sci. 17 (1986) 381–386.CrossRefGoogle Scholar
[4]Gregory, R. T. and Karney, D. L., A collection of matrices for testing computational algorithms (Wiley-Interscience, New York, 1969).Google Scholar
[5]Konavic, P., “Inversion of a covariance matrix”, J. Comput. Phys. 5 (1970) 355–357.Google Scholar
[6]Lietzke, M. H., Stoughton, R. W. and Lietzke, M. P., “A comparison of several methods for inverting large symmetric positive definite matrices”, Math. Comp. 18 (1964) 449–456.CrossRefGoogle Scholar
[7]Milnes, H. W., “A note concerning the properties of a certain class of test matrices”, Math. Comp. 22 (1968) 827–832.Google Scholar
[8]Newman, M. and Todd, J., “The evaluation of matrix inversion programs”, SIAM J. 6 (1958) 466–476.Google Scholar
[9]Picinbono, B., “Fast algorithms for Brownian matrices”, IEEE Trans. Acoust. Speech Signal Process. 31 (1983) 512–514.CrossRefGoogle Scholar
[10]Valvi, F. N., “Explicit presentation of some types of matrices”, J. Inst. Math. Appl. 19 (1977) 107–117.CrossRefGoogle Scholar
[11]Valvi, F. N. and Geronyannis, V. S., “Analytic inverses and determinants for a class of matrices”, IMA J. Numer. Anal. 7 (1987) 123–128.CrossRefGoogle Scholar