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2018•Mathematical Problems in EngineeringOpen access

A Method of Indefinite Krylov Subspace for Eigenvalue Problem

M. Aliyari, Mojtaba Ghasemi Kamalvand

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Abstract

We describe an indefinite state of Arnoldi’s method for solving the eigenvalues problems. In the following, we scrutinize the indefinite state of Lanczos’ method for solving the eigenvalue problems and we show that this method for the J -Hermitian matrices works much better than Arnoldi’s method.

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What this paper is about

We describe an indefinite state of Arnoldi’s method for solving the eigenvalues problems. In the following, we scrutinize the indefinite state of Lanczos’ method for solving the eigenvalue problems and we show that this method for the J -Hermitian matrices works much better than Arnoldi’s method.

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Available abstract

We describe an indefinite state of Arnoldi’s method for solving the eigenvalues problems. In the following, we scrutinize the indefinite state of Lanczos’ method for solving the eigenvalue problems and we show that this method for the J -Hermitian matrices works much better than Arnoldi’s method.

Key concepts: Krylov subspace, Eigenvalues and eigenvectors, Lanczos resampling, Arnoldi iteration, Hermitian matrix, Applied mathematics, Generalized minimal residual method, Mathematics

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