A New Quotient and Iterative Detection Method in an Affine Krylov Subspace for Solving Eigenvalue Problems

نویسندگان

چکیده

The paper solves the eigenvalues of a symmetric matrix by using three novel algorithms developed in m-dimensional affine Krylov subspace. n-dimensional eigenvector is superposed constant shifting vector and an m-vector. In first algorithm, m-vector derived as function eigenvalue maximizing Rayleigh quotient to generate characteristic equation, which, however, not easy determine since its roots are simple ones, exhibiting turning points, spikes, even no intersecting point zero line. To overcome that difficulty we propose second equation through new with inner product eigen-equation. Newton method fictitious time integration convergent very fast due equation. For both nonsymmetric problems solved third develop iterative detection maximize Euclidean norm terms eigen-parameter, which peaks response curve correspond eigenvalues. Through few finer tunings smaller intervals sequentially, accurate can be obtained. efficiency accuracy proposed verified compared Lanczos algorithm iteration method.

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ژورنال

عنوان ژورنال: Journal of Mathematics

سال: 2023

ISSN: ['2314-4785', '2314-4629']

DOI: https://doi.org/10.1155/2023/9859889