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The Computer Journal 1981 24(2):177-179; doi:10.1093/comjnl/24.2.177
© 1981 by British Computer Society
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The determination of eigenvalues of symmetric quindiagonal matrices

W. A. Sentance1 * and I. P. Cliff2 §

1 Department of Computer Science, The City University, Northampton Square, London, UK, 2 School of Mathematics and Computing, Slough College of Higher Education, Wellington Street, Slough, UK

Evans (1975) has described a method for finding the eigenvalues of quindiagonal matrices A based on the bisection and the Sturm sequence property of the leading principal minors Pi({lambda}) of A–{lambda}I. The algorithms there presented contained certain typographical errors, but even with these removed the procedures give incorrect results for certain matrices which have some zero Pi({lambda}) at the point of bisection. This paper describes a modification, based on earlier work on general band matrices, in which the sign of Pi({lambda}) is determined without calculating its value. Thus there are no problems with underflow or overflow.

Received April 1980.

* Department of Computer Science, The City University, Northampton Square, London EC1V 0HB.

§ School of Mathematics and Computing, Slough College of Higher Education, Wellington Street, Slough, Berkshire SL1 1YG.


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