Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems
نویسندگان
چکیده
منابع مشابه
Recycling Krylov Subspaces for Sequences of Linear Systems
Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two di erent approaches. For several model problems, we demonstrate that we can reduce the iteration count required to solve a linear system by a factor of two. We con...
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The most popular iterative linear solvers in Computational Fluid Dynamics (CFD) calculations are restarted GMRES and BiCGStab. At the beginning of most incompressible flow calculations, the computation time and the number of iterations to converge for the pressure Poisson equation are quite high, since the initial guess is far from the solution. In this case, the BiCGStab algorithm, with relati...
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We discuss the numerical solution of successive linear systems of equations Ax = bi, i = 1,2, . . .m, by iterative methods based on recycling Krylov subspaces. We propose various recycling algorithms which are based on the generalized conjugate residual (GCR) method. The recycling algorithms reuse the descent vectors computed while solving the previous linear systems Ax = b j, j = 1,2, . . . , ...
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by iterative methods based on recycling Krylov subspaces. We propose two recycling algorithms, which are both based on the generalized conjugate residual (GCR) method. The recycling methods reuse the descent vectors computed while solving the previous linear systems Ax = bj , j = 1, 2, . . . , i − 1, such that a lot of computational work can be saved when solving the current system Ax = bi. Whe...
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A standard approach to model reduction of large-scale higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for model reduction of first-order systems. This paper presents some results about the structure of the block-Krylov subspaces induced by the matrices of such equivalent first-order formulations of hig...
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ژورنال
عنوان ژورنال: ACM Transactions on Mathematical Software
سال: 2021
ISSN: 0098-3500,1557-7295
DOI: 10.1145/3439746