Application of Vector-valued Rational Approximations to the Matrix Eigenvalue Problem and Connections with Krylov Subspace MethodsLewis Research Center, Institute for Computational Mechanics in Propulsion, 1992 - Approximation theory - 33 pages |
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actually addition analytic applying arbitrary Arnoldi and Lanczos coefficients column combinations completes computational considered constant multiple constructions convergence corresponding invariant subspaces defective eigenvalues defined denominator denote detail determined developments eigenvectors elements equations equivalent extrapolation fact follows given implementation known Krylov subspace methods Lanczos method linear linearly independent Maclaurin series matrix eigenvalue problem mentioned methods of Arnoldi minimal polynomial multiple normal Numer observation obtained optimal approximations orthogonal particular pertaining poles polynomial power iterations power method precisely present principal projection methods proof properties rate of convergence rational function reciprocals REPORT respectively Ritz values Ritz vectors satisfy scalar Section shown Sidi simple SMMPE SMPE SMPE and STEA spaces span STEA procedures Step tend Theorem 3.1 theory Treatment turn upper vector-valued rational approximation vectors aji zeros