Expressions and Bounds for the GMRES Residual

[1]  Lloyd N. Trefethen,et al.  GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems , 2018, SIAM J. Sci. Comput..

[2]  Ilse C. F. Ipsen,et al.  THE IDEA BEHIND KRYLOV METHODS , 1998 .

[3]  Tobin A. Driscoll,et al.  From Potential Theory to Matrix Iterations in Six Steps , 1998, SIAM Rev..

[4]  Marlis Hochbruck,et al.  Error Analysis of Krylov Methods In a Nutshell , 1998, SIAM J. Sci. Comput..

[5]  M. Arioli,et al.  Krylov sequences of maximal length and convergence of GMRES , 1997 .

[6]  Zhi-Hao Cao,et al.  A note on the convergence behavior of GMRES , 1997 .

[7]  I. Moret.  A Note on the Superlinear Convergence of GMRES , 1997 .

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

[9]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[10]  Thomas A. Manteuffel,et al.  Minimal Residual Method Stronger than Polynomial Preconditioning , 1996, SIAM J. Matrix Anal. Appl..

[11]  Ming Gu,et al.  Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization , 1996, SIAM J. Sci. Comput..

[12]  Anne Greenbaum,et al.  Any Nonincreasing Convergence Curve is Possible for GMRES , 1996, SIAM J. Matrix Anal. Appl..

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

[14]  Homer F. Walker,et al.  A simpler GMRES , 1994, Numer. Linear Algebra Appl..

[15]  Anne Greenbaum,et al.  Max-Min Properties of Matrix Factor Norms , 1994, SIAM J. Sci. Comput..

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

[17]  Lloyd N. Trefethen,et al.  How Fast are Nonsymmetric Matrix Iterations? , 1992, SIAM J. Matrix Anal. Appl..

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

[19]  Ilse C. F. Ipsen,et al.  Perturbation Theory for the Solution of Systems of Linear Equations , 1991 .

[20]  Peter N. Brown,et al.  A Theoretical Comparison of the Arnoldi and GMRES Algorithms , 1991, SIAM J. Sci. Comput..

[21]  Willy Govaerts,et al.  A Singular Value Inequality for Block Matrices , 1989 .

[22]  W. Gautschi,et al.  Lower bounds for the condition number of Vandermonde matrices , 1987 .

[23]  G. Stewart.  Collinearity and Least Squares Regression , 1987 .

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

[25]  A. Greenbaum.  Comparison of splittings used with the conjugate gradient algorithm , 1979 .

[26]  R. Cottle.  On manifestations of the Schur complement , 1975 .

[27]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[28]  William Kahan,et al.  Some new bounds on perturbation of subspaces , 1969 .

[29]  Chandler Davis.  The rotation of eigenvectors by a perturbation , 1963 .

[30]  P. Henrici.  Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices , 1962 .

[31]  Ilse C. F. Ipsen.  A different approach to bounding the minimal residual norm in Krylov methods , 1998 .

[32]  Anne Greenbaum,et al.  Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.

[33]  H. Walker,et al.  GMRES On (Nearly) Singular Systems , 1997, SIAM J. Matrix Anal. Appl..

[34]  Kim-Chuan Toh,et al.  GMRES vs. Ideal GMRES , 1997, SIAM J. Matrix Anal. Appl..

[35]  INVERSE PROBLEMS NEWSLETTER , 1997 .

[36]  Ilse C. F. Ipsen,et al.  On the Sensitivity of Solution Components in Linear Systems of Equations , 1995, SIAM J. Matrix Anal. Appl..