GMRES/CR and Arnoldi/Lanczos as matrix approximation problems
Anne Greenbaum, Lloyd Nicholas Trefethen, Cornell Theory Center. Advanced Computing Research Institute
Cornell Theory Center, 1992 - Mathematics - 14 pages
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Analytic Function annihilating polynomial Approximation Problems Anne approximation theory Arnoldi algorithms Arnoldi and GMRES Arnoldi approximation problem Arnoldi iteration locates Arnoldi/Lanczos as Matrix behavior best approximants Chebyshev polynomial Comp complex plane constant term equivalent Existence and uniqueness field of values GMRES and Arnoldi GMRES and ideal GMRES approximation problem GMRES convergence curve GMRES curve GMRES polynomial q+ GMRES problems GMRES/CR and Arnoldi/Lanczos ideal Arnoldi polynomial ideal Arnoldi problem ideal GMRES convergence ideal GMRES polynomial initial guesses iteration locates eigenvalues iterative methods L. N. Trefethen Lanczos iterations Lawson's algorithm least-squares Lenferink-Spijker matrix Math Matrix Approximation Problems matrix iterations maximal singular value Maximizing the left-hand monic polynomial N. M. Nachtigal nonsingular nonzero normal matrices Numerical Analysis numerical linear algebra optimization orthonormal Pade approximation polynomials of degree pseudospectra q2 are minimal set A(A SIAM singular vectors solution step systems of equations Theorem true and ideal true GMRES polynomials vector norm