Abstract
This paper examines the solving of the eigenvalue problem for a matrix M (λ) with a nonlinear occurrence of the spectral parameter. Two methods are suggested for replacing the equation dat M(λ)=0 by a scalar equationf(λ)=0. Here the functionf(λ) is not written formally, but a rule for computingf(λ) at a fixed point of the domain in which the desired roots lie is indicated. Muller's method is used to solve the equationf(λ)=0. The eigenvalue found is refined by Newton's method based on the normalized expansion of matrix M(λ), and the linearly independent vectors corresponding to it are computed. An ALGOL program and test examples are presented.
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