منابع مشابه
Fractional Inversion in Krylov Space
The fractional inverse M (real γ > 0) of a matrix M is expanded in a series of Gegenbauer polynomials. If the spectrum of M is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for Mx = b in Krylov space. In case of γ = 1/2, the expansion is in t...
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We give an overview of various Lanczos/Krylov space methods and how they are being used for solving certain problems in Control Systems Theory based on state-space models. The matrix methods used are based on Krylov sequences and are closely related to modern iterative methods for standard matrix problems such as sets of linear equations and eigenvalue calculations. We show how these methods ca...
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We deal with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the source magnitude in the time fractional diffusion equation from viewpoint of numerics. Such simultaneous inversion problem is often of severe ill-posedness as compared with that of determining a single coefficient function. The forward problem is solved by employing an implicit finite...
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It will be shown that extended Krylov subspaces –under some assumptions– can be retrieved without any explicit inversion or system solves involved. Instead we do the necessary computations of A−1v in an implicit way using the information from an enlarged standard Krylov subspace. It is well-known that both for classical and extended Krylov spaces, direct unitary similarity transformations exist...
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ژورنال
عنوان ژورنال: Nuclear Physics B - Proceedings Supplements
سال: 1998
ISSN: 0920-5632
DOI: 10.1016/s0920-5632(97)00952-3