The determination of eigenvalues of symmetric quindiagonal matrices

Abstract

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(λ) of A−λI. 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(λ) at the point of bisection. This paper describes a modification, based on earlier work on general band matrices, in which the sign of Pi(λ) is determined without calculating its value. Thus there are no problems with underflow or overflow.