منابع مشابه
Augmented Block Householder Arnoldi Method
Computing the eigenvalues and eigenvectors of a large sparse nonsymmetric matrix arises in many applications and can be a very computationally challenging problem. In this paper we propose the Augmented Block Householder Arnoldi (ABHA) method that combines the advantages of a block routine with an augmented Krylov routine. A public domain MATLAB code ahbeigs has been developed and numerical exp...
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In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. We derive some useful a-posteriori bounds together with some hints for a suitable implementation inside the integrators. Numerical experiments arising from the discretization...
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Since version 2.4 of the RKToolbox, the rat krylov function can simulate the parallel construction of a rational Krylov basis. This is done by imposing various nonzero patterns in a so-called continuation matrix T . Simply speaking, the j-th column of this matrix contains the coefficients of the linear combination of j rational Krylov basis vectors which have been used to compute the next (j + ...
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A superlinear convergence bound for rational Arnoldi approximations to functions of matrices is derived. This bound generalizes the well-known superlinear convergence bound for the CG method to more general functions with finite singularities and to rational Krylov spaces. A constrained equilibrium problem from potential theory is used to characterize a max-min quotient of a nodal rational func...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2020
ISSN: 0895-4798,1095-7162
DOI: 10.1137/19m1245505