Multigrid Arnoldi for Eigenvalues
نویسندگان
چکیده
A new approach is given for computing eigenvalues and eigenvectors of large matrices. Multigrid is combined with the Arnoldi method in order to solve difficult problems. First, a two-grid method computes eigenvalues on a coarse grid and improves them on the fine grid. On the fine grid, an Arnoldi-type method is used that, unlike standard Arnoldi methods, can accept initial approximate eigenvectors. This approach can vastly improve Krylov computations. It also succeeds for problems that regular multigrid cannot handle. Analysis is given to explain why fine grid convergence rates can sometimes unexpectedly match that of regular Arnoldi. Near-Krylov theory is developed for this. Finally, this new method is generalized for more grid levels to produce a Multiple-grid Arnoldi method. AMS subject classifications. 65F15, 15A18
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