Lecture Notes on Solving Large Scale Eigenvalue Problems

[1]  Merico E. Argentati,et al.  Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc , 2007, SIAM J. Sci. Comput..

[2]  Gene H. Golub,et al.  Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.

[3]  M. Rozložník Numerics of Gram-Schmidt orthogonalization , 2007 .

[4]  U. Hetmaniuk,et al.  A comparison of eigensolvers for large‐scale 3D modal analysis using AMG‐preconditioned iterative methods , 2005 .

[5]  Heinrich Voss,et al.  A Jacobi-Davidson Method for Nonlinear Eigenproblems , 2004, International Conference on Computational Science.

[6]  G. W. Stewart,et al.  A Krylov-Schur Algorithm for Large Eigenproblems , 2001, SIAM J. Matrix Anal. Appl..

[7]  J. Cullum,et al.  Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1 , 2002 .

[8]  Andrew V. Knyazev,et al.  Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method , 2001, SIAM J. Sci. Comput..

[9]  G. Stewart Matrix Algorithms, Volume II: Eigensystems , 2001 .

[10]  A. Sameh,et al.  The trace minimization method for the symmetric generalized eigenvalue problem , 2000 .

[11]  Kesheng Wu,et al.  Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems , 2000, SIAM J. Matrix Anal. Appl..

[12]  Jack Dongarra,et al.  Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.

[13]  Gerard L. G. Sleijpen,et al.  Alternative correction equations in the Jacobi-Davidson method , 1999, Numer. Linear Algebra Appl..

[14]  Gerard L. G. Sleijpen,et al.  Jacobi-Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils , 1998, SIAM J. Sci. Comput..

[15]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[16]  Y. Feng,et al.  CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS , 1996 .

[17]  Gerard L. G. Sleijpen,et al.  A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM Rev..

[18]  S. Eisenstat,et al.  A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem , 1994, SIAM J. Matrix Anal. Appl..

[19]  J. Rodriguez,et al.  Problem (2) , 1994 .

[20]  B. Liu,et al.  [Effect of BN52021 on platelet activating factor induced aggregation of psoriatic polymorphonuclear neutrophils]. , 1994, Zhonghua yi xue za zhi.

[21]  D. Calvetti,et al.  AN IMPLICITLY RESTARTED LANCZOS METHOD FOR LARGE SYMMETRIC EIGENVALUE PROBLEMS , 1994 .

[22]  J. G. Lewis,et al.  A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems , 1994, SIAM J. Matrix Anal. Appl..

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

[24]  Ren-Cang Li Solving secular equations stably and efficiently , 1993 .

[25]  Danny C. Sorensen,et al.  Implicit Application of Polynomial Filters in a k-Step Arnoldi Method , 1992, SIAM J. Matrix Anal. Appl..

[26]  D. Sorensen,et al.  On the orthogonality of eigenvectors computed by divide-and-conquer techniques , 1991 .

[27]  R. Morgan Davidson's method and preconditioning for generalized eigenvalue problems , 1990 .

[28]  Christopher D. Beatie,et al.  Localization criteria and containment for Rayleigh quotient iteration , 1989 .

[29]  D. Szyld Criteria for Combining Inverse and Rayleigh Quotient Iteration , 1988 .

[30]  Jack J. Dongarra,et al.  An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.

[31]  Jack J. Dongarra,et al.  A proposal for a set of level 3 basic linear algebra subprograms , 1987, SGNM.

[32]  Ahmed H. Sameh,et al.  Trace Minimization Algorithm for the Generalized Eigenvalue Problem , 1982, PPSC.

[33]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[34]  H. Schwarz Rayleigh-Quotient-Minimierung mit Vorkonditionierung , 1987 .

[35]  R. Morgan,et al.  Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices , 1986 .

[36]  Jack J. Dongarra,et al.  A fully parallel algorithm for the symmetric eigenvalue problem , 1985, PPSC.

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

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

[39]  V. A. Barker,et al.  Finite element solution of boundary value problems , 1984 .

[40]  H. Schwarz Methode der finiten Elemente , 1984 .

[41]  H. Simon The Lanczos algorithm with partial reorthogonalization , 1984 .

[42]  G. Golub Matrix computations , 1983 .

[43]  B. Parlett The Symmetric Eigenvalue Problem , 1981 .

[44]  D. Longsine,et al.  Simultaneous rayleigh-quotient minimization methods for Ax=λBx , 1980 .

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

[46]  J. Cuppen A divide and conquer method for the symmetric tridiagonal eigenproblem , 1980 .

[47]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.

[48]  Jack J. Dongarra,et al.  Matrix Eigensystem Routines — EISPACK Guide Extension , 1977, Lecture Notes in Computer Science.

[49]  E. Davidson The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[50]  Ronald L. Graham,et al.  Problem #7 , 1974, SIGS.

[51]  Axel Ruhe ALGORITHMS FOR THE NONLINEAR EIGENVALUE PROBLEM , 1973 .

[52]  William G. Poole,et al.  A geometric theory for the QR, LU and power iterations. , 1973 .

[53]  H. Rutishauser Simultaneous iteration method for symmetric matrices , 1970 .

[54]  N. Meyers,et al.  H = W. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[55]  P. P. Starling The numerical solution of Laplace's equation , 1963 .

[56]  D. Faddeev,et al.  Computational Methods of Linear Algebra. , 1966, The Mathematical Gazette.

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

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

[59]  C. Jacobi Über ein leichtes Verfahren die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen*). , 2022 .