Closer to the solution : Iterative linear solversGene

[1]  H. V. D. Vorst,et al.  The rate of convergence of Conjugate Gradients , 1986 .

[2]  O. Nevanlinna,et al.  Accelerating with rank-one updates , 1989 .

[3]  T. Manteuffel.  The Tchebychev iteration for nonsymmetric linear systems , 1977 .

[4]  Vijay Sonnad,et al.  A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations , 1989 .

[5]  Gene H. Golub,et al.  Some History of the Conjugate Gradient and Lanczos Algorithms: 1948-1976 , 1989, SIAM Rev..

[6]  Roland W. Freund,et al.  A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems , 1993, SIAM J. Sci. Comput..

[7]  A. Griewank,et al.  Approximate inverse preconditionings for sparse linear systems , 1992 .

[8]  S. Eisenstat,et al.  Variational Iterative Methods for Nonsymmetric Systems of Linear Equations , 1983 .

[9]  Wei-Pai Tang,et al.  Ordering Methods for Preconditioned Conjugate Gradient Methods Applied to Unstructured Grid Problems , 1992, SIAM J. Matrix Anal. Appl..

[10]  G. Golub,et al.  Block Preconditioning for the Conjugate Gradient Method , 1985 .

[11]  H. V. D. Vorst,et al.  Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems☆ , 1981 .

[12]  E. Sturler,et al.  Nested Krylov methods based on GCR , 1996 .

[13]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[14]  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..

[15]  Roland W. Freund,et al.  An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices , 1993, SIAM J. Sci. Comput..

[16]  H. Elman.  Iterative methods for large, sparse, nonsymmetric systems of linear equations , 1982 .

[17]  G. Golub,et al.  The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems , 1988 .

[18]  Yousef Saad,et al.  ILUT: A dual threshold incomplete LU factorization , 1994, Numer. Linear Algebra Appl..

[19]  H. V. D. Vorst,et al.  A Petrov-Galerkin type method for solving Axk=b, where A is symmetric complex , 1990 .

[20]  Yvan Notay,et al.  DRIC: A dynamic version of the RIC method , 1994, Numer. Linear Algebra Appl..

[21]  C. Lanczos.  Solution of Systems of Linear Equations by Minimized Iterations1 , 1952 .

[22]  T. Chan,et al.  An analysis of the composite step biconjugate gradient method , 1993 .

[23]  Gene H. Golub,et al.  Inner and Outer Iterations for the Chebyshev Algorithm , 1998 .

[24]  H. V. D. Vorst,et al.  High Performance Preconditioning , 1989 .

[25]  O. Axelsson.  Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations , 1980 .

[26]  I. Gustafsson.  A class of first order factorization methods , 1978 .

[27]  O. Axelsson,et al.  A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning , 1991 .

[28]  H. V. D. Vorst,et al.  Generalized conjugate gradient squared , 1996 .

[29]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[30]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[31]  Yves Robert,et al.  Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor , 1989, Parallel Comput..

[32]  Tony F. Chan,et al.  A Note on the Efficiency of Domain Decomposed Incomplete Factorizations , 1990, SIAM J. Sci. Comput..

[33]  G. Golub,et al.  Inexact and preconditioned Uzawa algorithms for saddle point problems , 1994 .

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

[35]  D. Hut.  A Newton Basis Gmres Implementation , 1991 .

[36]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[37]  Cornelis Vuik,et al.  GMRESR: a family of nested GMRES methods , 1994, Numer. Linear Algebra Appl..

[38]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[39]  Homer F. Walker,et al.  Residual Smoothing Techniques for Iterative Methods , 1994, SIAM J. Sci. Comput..

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

[41]  Claude Pommerell,et al.  Solution of large unsymmetric systems of linear equations , 1992 .

[42]  R. Pavani,et al.  Parallel Numerical Linear Algebra , 1995, PDP.

[43]  Shao-Liang Zhang,et al.  GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems , 1997, SIAM J. Sci. Comput..

[44]  Takumi Washio,et al.  Parallel block preconditioning based on SSOR and MILU , 1994, Numer. Linear Algebra Appl..

[45]  YereminA. Yu.,et al.  Factorized sparse approximate inverse preconditionings I , 1993 .

[46]  B. Fischer.  Polynomial Based Iteration Methods for Symmetric Linear Systems , 1996 .

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

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

[49]  D. R. Fokkema,et al.  BICGSTAB( L ) FOR LINEAR EQUATIONS INVOLVING UNSYMMETRIC MATRICES WITH COMPLEX , 1993 .

[50]  G. Golub,et al.  How to generate unknown orthogonal polynomials out of known orthogonal polynomials , 1992 .

[51]  A. Bruaset.  A survey of preconditioned iterative methods , 1995 .

[52]  G. Golub,et al.  Iterative solution of linear systems , 1991, Acta Numerica.

[53]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[54]  G. Golub,et al.  Estimates of Eigenvalues for Iterative Methods , 1989 .

[55]  J. Ortega,et al.  SOR as a preconditioner , 1995 .

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

[57]  Magolu Monga-Made.  Ordering strategies for modified block incomplete factorizations , 1995 .

[58]  P. Sonneveld.  CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems , 1989 .

[59]  Fred Wubs,et al.  Nested grids ILU-decomposition (NGILU) , 1996 .

[60]  Roland W. Freund,et al.  Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices , 1992, SIAM J. Sci. Comput..

[61]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[62]  Gene H. Golub,et al.  Line Iterative Methods for Cyclically Reduced Discrete Convection-Diffusion Problems , 1992, SIAM J. Sci. Comput..

[63]  O. Axelsson,et al.  On the eigenvalue distribution of a class of preconditioning methods , 1986 .

[64]  O. Widlund.  A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations , 1978 .

[65]  Zhishun A. Liu,et al.  A Look Ahead Lanczos Algorithm for Unsymmetric Matrices , 1985 .

[66]  J. Meijerink,et al.  Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems , 1981 .

[67]  Martin H. Gutknecht,et al.  A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I , 1992, SIAM J. Matrix Anal. Appl..

[68]  Kang C. Jea,et al.  Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods , 1980 .

[69]  Y. Saad,et al.  Approximate inverse preconditioners for general sparse matrices , 1994 .

[70]  Monga-Made Magolu.  Modified block-approximate factorization strategies , 1992 .

[71]  O. Axelsson.  Solution of linear systems of equations: Iterative methods , 1977 .

[72]  H. V. D. Vorst,et al.  A comparison of some GMRES-like methods , 1992 .

[73]  E. Desturler,et al.  Nested Krylov methods and preserving the orthogonality , 1993 .

[74]  P. K. W. Vinsome,et al.  Orthomin, an Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations , 1976 .

[75]  Avram Sidi,et al.  Efficient implementation of minimal polynomial and reduced rank extrapolation methods , 1991 .

[76]  Martin H. Gutknecht,et al.  Variants of BICGSTAB for Matrices with Complex Spectrum , 1993, SIAM J. Sci. Comput..

[77]  C. G. Broyden.  A New Method of Solving Nonlinear Simultaneous Equations , 1969, Comput. J..

[78]  Wolfgang Fichtner,et al.  PILS: an iterative linear solver package for ill-conditioned systems , 1991, Proceedings of the 1991 ACM/IEEE Conference on Supercomputing (Supercomputing '91).

[79]  Henk A. van der Vorst,et al.  Large tridiagonal and block tridiagonal linear systems on vector and parallel computers , 1987, Parallel Comput..

[80]  Howard C. Elman,et al.  Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems , 1989 .