On restarting the tensor infinite Arnoldi method
نویسندگان
چکیده
منابع مشابه
The Waveguide Eigenvalue Problem and the Tensor Infinite Arnoldi Method
We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the tensor infinite Arnoldi method (TIAR), which is applicable to a general class of NEPs, and we show how to specialize the algorithm to a specific NEP: the wavegui...
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The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired. We analyze several approaches to restarting and show why Sorensen’s implicit QR approach is g...
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The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a technique to compute a partial Schur factorization of a nonlinear eigenvalue problem (NEP). The technique is inspired by the algorithm in [8], now called the infini...
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The Davidson method is a popular preconditioned variant of the Arnoldi method for solving large eigenvalue problems. For theoretical, as well as practical reasons the two methods are often used with restarting. Frequently, information is saved through approximated eigen-vectors to compensate for the convergence impairment caused by restarting. We call this scheme of retaining more eigenvectors ...
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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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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2017
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-017-0671-z