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An application of the homotopy method to the generalised symmetric eigenvalue problem

Published online by Cambridge University Press:  17 February 2009

Wen-Wei Lin  and
Gerhard Lutzer
Wen-Wei Lin
Affiliation:
Institute of Applied Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
Gerhard Lutzer
Affiliation:
Institute of Applied Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
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Abstract

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The homotopy method is used to find all eigenpairs of a generalised symmetric eigenvalue problem Ax = λBx with positive definite B. The determination of n eigenpairs (x, λ) is reduced to curve tracing of n disjoint smooth curves in Rn × R × [0, 1]. The method might be attractive if A and B are sparse symmetric. In this paper it is shown that the method will work for almost all symmetric tridiagonal matrices A and B.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 2 , October 1988 , pp. 230 - 249
Copyright
Copyright © Australian Mathematical Society 1988

References

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