Abstract perturbed Krylov methods

[1]  C. Lanczos.  An iteration method for the solution of the eigenvalue problem of linear differential and integral operators , 1950 .

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

[3]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[4]  E. Stiefel,et al.  Relaxationsmethoden bester Strategie zur Lösung linearer Gleichungssysteme , 1955 .

[5]  Eigenvectors obtained from the adjoint matrix , 1968 .

[6]  Olga Taussky.  The factorization of the adjugate of a finite matrix , 1968 .

[7]  Christopher C. Paige,et al.  The computation of eigenvalues and eigenvectors of very large sparse matrices , 1971 .

[8]  C. Paige.  Computational variants of the Lanczos method for the eigenproblem , 1972 .

[9]  C. Paige.  Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix , 1976 .

[10]  C. Paige.  Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem , 1980 .

[11]  J. Grcar.  Analyses of the lanczos algorithm and of the approximation problem in richardson's method , 1981 .

[12]  H. Simon.  Analysis of the symmetric Lanczos algorithm with reorthogonalization methods , 1984 .

[13]  J. Cullum,et al.  Lanczos algorithms for large symmetric eigenvalue computations , 1985 .

[14]  On the Matrix Adjoint (Adjugate) , 1985 .

[15]  A. Greenbaum.  Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences , 1989 .

[16]  T. Manteuffel,et al.  A taxonomy for conjugate gradient methods , 1990 .

[17]  R. Morgan.  Computing Interior Eigenvalues of Large Matrices , 1991 .

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

[19]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[20]  R. Freund.  Quasi-kernel polynomials and their use in non-Hermitian matrix iterations , 1992 .

[21]  Anne Greenbaum,et al.  Predicting the Behavior of Finite Precision Lanczos and Conjugate Gradient Computations , 2015, SIAM J. Matrix Anal. Appl..

[22]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[23]  Gerard L. G. Sleijpen,et al.  Krylov subspace methods for large linear systems of equations , 1993 .

[24]  B. Parlett,et al.  Semi-duality in the two-sided lanczos algorithm , 1993 .

[25]  Zhaojun Bai,et al.  Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem , 1994 .

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

[27]  C. G. Broyden.  A new taxonomy of conjugate gradient methods , 1996 .

[28]  Anne Greenbaum,et al.  Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems , 1996, SIAM J. Matrix Anal. Appl..

[29]  A. Greenbaum.  Estimating the Attainable Accuracy of Recursively Computed Residual Methods , 1997, SIAM J. Matrix Anal. Appl..

[30]  D. Day,et al.  An Efficient Implementation of the Nonsymmetric Lanczos Algorithm , 1997 .

[31]  Martin H. Gutknecht,et al.  Lanczos-type solvers for nonsymmetric linear systems of equations , 1997, Acta Numerica.

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

[33]  Qiang Ye,et al.  Analysis of the finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems , 2000, Math. Comput..

[34]  Valeria Simoncini,et al.  On the Convergence of Restarted Krylov Subspace Methods , 2000, SIAM J. Matrix Anal. Appl..

[35]  M. Eiermann,et al.  Geometric aspects of the theory of Krylov subspace methods , 2001, Acta Numerica.

[36]  C. Brezinski,et al.  A review of formal orthogonality in Lanczos-based methods , 2002 .

[37]  J. Liesen,et al.  Least Squares Residuals and Minimal Residual Methods , 2001, SIAM J. Sci. Comput..

[38]  Valeria Simoncini,et al.  Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing , 2003, SIAM J. Sci. Comput..

[39]  Jens-Peter M. Zemke,et al.  Krylov Subspace Methods in Finite Precision : A Unified Approach , 2003 .

[40]  Gerard L. G. Sleijpen,et al.  Inexact Krylov Subspace Methods for Linear Systems , 2004, SIAM J. Matrix Anal. Appl..

[41]  Maria Teresa Vespucci,et al.  Krylov Solvers for Linear Algebraic Systems: Krylov Solvers , 2004 .

[42]  Valérie Frayssé,et al.  Inexact Matrix-Vector Products in Krylov Methods for Solving Linear Systems: A Relaxation Strategy , 2005, SIAM J. Matrix Anal. Appl..

[43]  G. Meurant.  The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations , 2006 .

[44]  J. Zemke.  (Hessenberg) eigenvalue-eigenmatrix relations , 2006 .

[45]  G. Meurant,et al.  The Lanczos and conjugate gradient algorithms in finite precision arithmetic , 2006, Acta Numerica.