Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method
نویسندگان
چکیده
منابع مشابه
Controlling Inner Iterations in the Jacobi-Davidson Method
The Jacobi–Davidson method is an eigenvalue solver which uses the iterative (and in general inaccurate) solution of inner linear systems to progress, in an outer iteration, towards a particular solution of the eigenproblem. In this paper we prove a relation between the residual norm of the inner linear system and the residual norm of the eigenvalue problem. We show that the latter may be estima...
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The spectral transformation Lanczos method and the shift-invert Arnoldi method are probably the most popular methods for the solution of linear generalized eigenvalue problems originating from engineering applications, including structural and acoustic analyses and fluid dynamics. The orthogonalization of the Krylov vectors requires inner products. Often, one employs the standard inner product,...
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The Jacobi–Davidson method is a popular technique to compute a few eigenpairs of large sparse matrices. Its introduction, about a decade ago, was motivated by the fact that standard eigensolvers often require an expensive factorization of the matrix to compute interior eigenvalues. Such a factorization may be infeasible for large matrices as arise in today’s large-scale simulations. In the Jaco...
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The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower t...
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ژورنال
عنوان ژورنال: Science China Mathematics
سال: 2014
ISSN: 1674-7283,1869-1862
DOI: 10.1007/s11425-014-4791-5