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- W4247371302 abstract "This edition of Problems and Techniques features articles on convergence anomalies in restarted GMRES and determining the eigenvalues of the Laplacian on triangles. GMRES has become a mainstay in solving large, sparse, unsymmetric linear algebraic systems. Because of the increase in per-iteration cost, GMRES is frequently restarted after a given number m iterations, using the last result as the new initial guess. The larger m, the faster the convergence, right? Wrong! Mark Embree, the author of our first feature, provides us with a host of examples where restarting more frequently enhances convergence. While the theory behind this phenomenon is not yet available, Embree shows us that restarted GMRES can be very sensitive to the initial residual. In our second article, Brian McCartin enlightens us on Lamé's formulas for the eigenvalues of the Laplacian with Dirichlet conditions on a triangle. I plead ignorance. I didn't realize such things existed. However, Lamé provided the formulas, and now, 170 years later, McCartin shows us how to derive them. He provides additional information about the spectrum and nodal lines and concludes with a biography of Lamé. Happy reading." @default.
- W4247371302 created "2022-05-12" @default.
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- W4247371302 date "2003-01-01" @default.
- W4247371302 modified "2023-09-27" @default.
- W4247371302 title "Problems and Techniques" @default.
- W4247371302 doi "https://doi.org/10.1137/siread000045000002000257000001" @default.
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