Greenbaum, AnneTrefethen, Lloyd N.2007-04-032007-04-031992-06http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/92-096https://hdl.handle.net/1813/5473The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize ||p(A)b|| over polynomials p of degree n. The difference is that p is nor- malized at z=0 for GMRES and at z=infinity for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes ||p(A)|| instead. Investigation of these true and ideal approximation problems gives insight into how fast GMRES converges and how the Arnoldi iteration locates eigenvalues.195079 bytes573011 bytesapplication/pdfapplication/postscripten-UStheory centertechnical report