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The Computer Journal 1975 18(1):70-73; doi:10.1093/comjnl/18.1.70
© 1975 by British Computer Society
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A recursive algorithm for determining the eigenvalues of a quindiagonal matrix

D. J. Evans *

Department of Computer Studies, Loughborough University of Technology, Loughborough, UK

A recursive algorithm for the implicit derivation of the determinant of a quindiagonal matrix is derived in terms of its leading principal minors. Its form is more compact and simpler than that previously presented in the literature by Sweed (1969). Its envisaged use is for deriving the eigenvalues of quindiagonal matrices by Newton's or similar root finding methods.

The derived algorithm simplifies considerably for the case of symmetric matrices yielding a Sturmian sequence of polynomials from which the eigenvalues can be obtained by used of the well known bisection process.

Received May 1973.

* Department of Mathematics, Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU


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