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On Gaussian elimination and determinant formulas for matrices with chordal inverses

Published online by Cambridge University Press:  17 April 2009

Mihály Bakonyi
Mihály Bakonyi
Affiliation:
Department of Mathematics, The College of William and Mary, Williamsburg VA 23187-8795, United States of America
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Abstract

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In this paper a formula is obtained for the entries of the diagonal factor in the U D L factorisation of an invertible operator matrix in the case when its inverse has a chordal graph. As a consequence, in the finite dimensional case a determinant formula is obtained in terms of some key principal minors. After a cancellation process this formula leads to a determinant formula from an earlier paper by W.W. Barrett and C.R. Johnson, deriving in this way a different and shorter proof of their result. Finally, an algorithmic method of constructing minimal vertex separators of chordal graphs is presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 3 , December 1992 , pp. 435 - 440
Copyright
Copyright © Australian Mathematical Society 1992

References

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