RITZ AND PSEUDO-RITZ VALUES USING MATRIX POLYNOMIALS

[1]  Ilse C. F. Ipsen,et al.  GMRES and the minimal polynomial , 1996 .

[2]  Walter Van Assche,et al.  Orthogonal matrix polynomials and applications , 1996 .

[3]  Avram Sidi,et al.  Application of Vector-Valued Rational Approximations to the Matrix Eigenvalue Problem and Connections with Krylov Subspace Methods , 1995, SIAM J. Matrix Anal. Appl..

[4]  Efstratios Gallopoulos,et al.  An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides , 1995, SIAM J. Sci. Comput..

[5]  Henk A. van der Vorst,et al.  Approximate solutions and eigenvalue bounds from Krylov subspaces , 1995, Numer. Linear Algebra Appl..

[6]  Thomas A. Manteuffel,et al.  On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method , 1994, Numer. Linear Algebra Appl..

[7]  Horst D. Simon,et al.  A New Approach to Construction of Efficient Iterative Schemes for Massively Parallel Applications: Variable Block CG and BiCG Methods and Variable Block Arnoldi Procedure , 1993, PPSC.

[8]  M. Sadkane A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices , 1993 .

[9]  H. V. D. Vorst,et al.  The superlinear convergence behaviour of GMRES , 1993 .

[10]  Lloyd N. Trefethen,et al.  A Hybrid GMRES Algorithm for Nonsymmetric Linear Systems , 1992, SIAM J. Matrix Anal. Appl..

[11]  L. Schumaker,et al.  Numerical methods in approximation theory , 1992 .

[12]  B. Vital Etude de quelques methodes de resolution de problemes lineaires de grande taille sur multiprocesseur , 1990 .

[13]  L. Trefethen Approximation theory and numerical linear algebra , 1990 .

[14]  Mark David Kent Chebyshev, Krylov, Lanczos : matrix relationships and computations , 1989 .

[15]  F. Chatelin Valeurs propres de matrices , 1988 .

[16]  J. Mason,et al.  Algorithms for approximation , 1987 .

[17]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[18]  J. Maroulas Factorization of matrix polynomials with multiple roots , 1985 .

[19]  Y. Saad Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices , 1980 .

[20]  Y. Saad On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods , 1980 .

[21]  J. G. Lewis Algorithms for sparse matrix eigenvalue problems , 1977 .

[22]  W. Arnoldi The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .