Abstract
In this paper, we consider descent iterations with line search for improving an approximate eigenvalue and a corresponding approximate eigenvector of polynomial eigenvalue problems with general complex matrices, where an approximate eigenpair was obtained by some method. The polynomial eigenvalue problem is written as a system of complex nonlinear equations with nondifferentiable normalized condition. Convergence theorems for iterations are established. Finally, some numerical examples are presented to demonstrate the effectiveness of the iterative methods.
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Received April 9, 2001; revised October 2, 2001 Published online February 18, 2002
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Ishihara, K. Descent Iterations for Improving Approximate Eigenpairs of Polynomial Eigenvalue Problems with General Complex Matrices. Computing 68, 239–254 (2002). https://doi.org/10.1007/s00607-001-1435-8
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DOI: https://doi.org/10.1007/s00607-001-1435-8