Geometric aspects of the theory of Krylov subspace methods
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[1] C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators , 1950 .
[2] M. Hestenes,et al. Methods of conjugate gradients for solving linear systems , 1952 .
[3] C. Lanczos. Solution of Systems of Linear Equations by Minimized Iterations1 , 1952 .
[4] Tosio Kato. Estimation of Iterated Matrices, with application to the von Neumann condition , 1960 .
[5] Chandler Davis. The rotation of eigenvectors by a perturbation , 1963 .
[6] Alston S. Householder,et al. The Theory of Matrices in Numerical Analysis , 1964 .
[7] R. Meyer,et al. Topics in the analytic theory matrices , 1967 .
[8] W. Kahan,et al. The Rotation of Eigenvectors by a Perturbation. III , 1970 .
[9] J. Ringrose. Compact non-self-adjoint operators , 1971 .
[10] T. N. E. Greville,et al. Solutions of the Matrix Equation $XAX = X$, and Relations between Oblique and Orthogonal Projectors , 1974 .
[11] M. Saunders,et al. Solution of Sparse Indefinite Systems of Linear Equations , 1975 .
[12] T. Manteuffel. The Tchebychev iteration for nonsymmetric linear systems , 1977 .
[13] R. Winther. Some Superlinear Convergence Results for the Conjugate Gradient Method , 1980 .
[14] Y. Saad. Krylov subspace methods for solving large unsymmetric linear systems , 1981 .
[15] Y. Saad. The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems , 1982 .
[16] H. Elman. Iterative methods for large, sparse, nonsymmetric systems of linear equations , 1982 .
[17] S. Eisenstat,et al. Variational Iterative Methods for Nonsymmetric Systems of Linear Equations , 1983 .
[18] P. Wedin. On angles between subspaces of a finite dimensional inner product space , 1983 .
[19] Gene H. Golub,et al. Matrix computations , 1983 .
[20] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .
[21] Leslie Greengard,et al. A fast algorithm for particle simulations , 1987 .
[22] W. Hackbusch,et al. On the fast matrix multiplication in the boundary element method by panel clustering , 1989 .
[23] P. Sonneveld. CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .
[24] O. Nevanlinna,et al. Accelerating with rank-one updates , 1989 .
[25] T. Manteuffel,et al. A taxonomy for conjugate gradient methods , 1990 .
[26] Peter N. Brown,et al. A Theoretical Comparison of the Arnoldi and GMRES Algorithms , 1991, SIAM J. Sci. Comput..
[27] Charles R. Johnson,et al. Topics in Matrix Analysis , 1991 .
[28] H. A. van der Vorst,et al. GMRESR : A family of nested GMRES methods Report 91-80 , 1991 .
[29] R. Freund,et al. QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .
[30] R. Freund. Quasi-kernel polynomials and their use in non-Hermitian matrix iterations , 1992 .
[31] 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..
[32] G. Golub,et al. Iterative solution of linear systems , 1991, Acta Numerica.
[33] Martin H. Gutknecht,et al. Variants of BICGSTAB for Matrices with Complex Spectrum , 1993, SIAM J. Sci. Comput..
[34] Michael Eiermann,et al. Fields of values and iterative methods , 1993 .
[35] Martin H. Gutknecht,et al. Changing the norm in conjugate gradient type algorithms , 1993 .
[36] Yousef Saad,et al. A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..
[37] Roland W. Freund,et al. A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems , 1993, SIAM J. Sci. Comput..
[38] Roland W. Freund,et al. An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices , 1993, SIAM J. Sci. Comput..
[39] Cornelis Vuik,et al. GMRESR: a family of nested GMRES methods , 1994, Numer. Linear Algebra Appl..
[40] Rüdiger Weiss,et al. Properties of generalized conjugate gradient methods , 1994, Numer. Linear Algebra Appl..
[41] Tony F. Chan,et al. A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems , 1994, SIAM J. Sci. Comput..
[42] G. Golub,et al. Recent advances in iterative methods , 1994 .
[43] Wayne Joubert,et al. On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems , 1994, Numer. Linear Algebra Appl..
[44] Homer F. Walker,et al. A simpler GMRES , 1994, Numer. Linear Algebra Appl..
[45] R. Freund,et al. Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems , 1994 .
[46] Homer F. Walker,et al. Residual Smoothing Techniques for Iterative Methods , 1994, SIAM J. Sci. Comput..
[47] Homer F. Walker,et al. Residual smoothing and peak/plateau behavior in Krylov subspace methods , 1995 .
[48] Miroslav Tuma,et al. On the Role of Orthogonality in the GMRES Method , 1996, SOFSEM.
[49] K. Gustafson,et al. Numerical Range: The Field Of Values Of Linear Operators And Matrices , 1996 .
[50] Anne Greenbaum,et al. Any Nonincreasing Convergence Curve is Possible for GMRES , 1996, SIAM J. Matrix Anal. Appl..
[51] B. Fischer. Polynomial Based Iteration Methods for Symmetric Linear Systems , 1996 .
[52] Anne Greenbaum,et al. Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems , 1996, SIAM J. Matrix Anal. Appl..
[53] I. Moret. A Note on the Superlinear Convergence of GMRES , 1997 .
[54] G. Starke. Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems , 1997 .
[55] M. Rozložník,et al. Numerical behaviour of the modified gram-schmidt GMRES implementation , 1997 .
[56] Martin H. Gutknecht,et al. Lanczos-type solvers for nonsymmetric linear systems of equations , 1997, Acta Numerica.
[57] Gene H. Golub,et al. Closer to the solutions: iterative linear solvers , 1997 .
[58] M. SIAMJ.,et al. RESIDUAL-MINIMIZING KRYLOV SUBSPACE METHODS FOR STABILIZED DISCRETIZATIONS OF CONVECTION-DIFFUSION EQUATIONS∗ , 1998 .
[59] Marlis Hochbruck,et al. Error Analysis of Krylov Methods In a Nutshell , 1998, SIAM J. Sci. Comput..
[60] Martin H. Gutknecht,et al. QMR Smoothing for Lanczos-Type Product Methods Based on Three-Term Rrecurrences , 1998, SIAM J. Sci. Comput..
[61] Yousef Saad,et al. Modified Krylov acceleration for parallel environments , 1999 .
[62] M. Embree. How Descriptive are GMRES Convergence Bounds? , 1999, ArXiv.
[63] G. Meurant. Computer Solution of Large Linear Systems , 1999 .
[64] E. Sturler,et al. Truncation Strategies for Optimal Krylov Subspace Methods , 1999 .
[65] Y. Saad,et al. Iterative solution of linear systems in the 20th century , 2000 .
[66] Jörg Liesen,et al. Computable Convergence Bounds for GMRES , 2000, SIAM J. Matrix Anal. Appl..
[67] Ronald B. Morgan,et al. Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations , 2000, SIAM J. Matrix Anal. Appl..
[68] Oliver G. Ernst,et al. Analysis of acceleration strategies for restarted minimal residual methods , 2000 .
[69] Yousef Saad. Further analysis of minimum residual iterations , 2000, Numer. Linear Algebra Appl..
[70] Yousef Saad,et al. Iterative methods for sparse linear systems , 2003 .