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We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG).
Methods of conjugate gradient for solving linear systems
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Confinement of quarks
Kenneth G. Wilson · 1974
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Multi-level adaptive solutions to boundary-value problems
A. Brandt · 1977
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The block Lanczos method for computing eigenvalues
G. H. Golub and R. Underwood · 1977
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The block conjugate gredient algorithm and related methods
Dianne P. O’Leary · 1980
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Iteration methods in eigenvalue problems
E. G. D’yakonov · 1983
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Algebraic multigrid theory: The symmetric case
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Practical Optimization
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GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
Y. Saad and M. H. Schultz · 1986
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Deflation of conjugate gradients with applications to boundary value problems
R. A. Nicolaides · 1987
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On the Lanczos method for solving symmetric linear systems with several right-hand sides
Y. Saad · 1987
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Preconditioned conjugate gradient for solving singular systems
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Convergence rate estimates for iteratime methods for symmetric eigenvalue problems and its implementation in a subspace
A. V. Knyazev · 1990
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Projective multigrid method for propagators in lattice gauge theory
Richard C. Brower, Claudio Rebbi, and Ettore Vicari · 1991
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Improved algorithms for the lowest eigenvalues and associated eigenvectors of large matrices
C. W. Murray, S. C. Racine, and E. R. Davidson · 1992
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Implicit application of polynomial filters in a K-step Arnoldi method
D. C. Sorensen · 1992
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An iterative method for nonsymmetric systems with multiple right-hand side
V. Simoncini and E. Gallopoulos · 1995
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Progress on lattice qcd algorithms
P. de Forcrand · 1996
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A parallel ssor preconditioner for lattice qcd
S. Fischer et al · 1996
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Matrix Computations
G. H. Golub and C. F. Van Loan · 1996
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Chronological inversion method for the dirac matrix in hybrid monte carlo
R. C. Brower, T. Ivanenko, A. R. Levi, and K. N. Orginos · 1997
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Analysis of projection methods for solving linear systems with multiple right-hand sides
Tony F. Chan and W.L. Wan · 1997
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A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
Roland W. Freund and Manish Malhotra · 1997
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GMRES with deflated restarting
R. B. Morgan · 2002
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Iterative methods for sparse linear systems
Y. Saad · 2003
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Improving meson two-point functions in lattice qcd
Thomas A. DeGrand and Stefan Schaefer · 2004
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Low-energy couplings of qcd from current correlators near the chiral limit
L. Giusti, P. Hernandez, M. Laine, P. Weisz, and H. Wittig · 2004
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The block lanczos method for linear systems with multiple right-hand sides
A. El Guennouni, K. Jbilou, and H. Sadok · 2004
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Deflated iterative methods for linear equations with multiple right-hand sides
R. Morgan and W. Wilcox · 2004
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Linear systems solvers - recent developments and implications for lattice computations
Andreas Frommer · 1997
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The geometry of algorithms with orthogonality constraints
A. Edelman, T. A. Arias, and S. T. Smith · 1998
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ARPACK User’s guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
R. B. Lehoucq, D. C. Sorensen, and C. Yang · 1998
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The Symmetric Eigenvalue Problem
B. N. Parlett · 1998
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Restarting techniques for (Jacobi-)Davidson symmetric eigenvalue methods
A. Stathopoulos and Y. Saad · 1998
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Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods
A. Stathopoulos, Y. Saad, and K. Wu · 1998
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Adaptive algebraic multigrid coarsening strategies
J Brannick · 2005
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Using spectral low rank preconditioners for large electromagnetic calculations
I. S. Duff, L. Giraud, J. Langou, and E. Martin · 2005
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The chroma software system for lattice qcd
Robert G. Edwards and Balint Joo · 2005
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Practical all-to-all propagators for lattice qcd
Justin Foley et al · 2005
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Extending the applicability of multigrid methods
J Brannick, M Brezina, R Falgout, T Manteuffel, S McCormick, J Ruge, B Sheehan, J Xu, and L Zikatanov · 2006
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Stability of lattice qcd simulations and the thermodynamic limit
L. Del Debbio, L. Giusti, M. Lüscher, R. Petronzio, and N. Tantalo · 2006
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A comparative study of iterative solvers exploiting spectral information for SPD systems
L. Giraud, D. Ruiz, and A. Touhami · 2006
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Block krylov space methods for linear systems with multiple right-hand sides: an introduction
Martin H. Gutknecht · 2006
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Polynomial filtering for hmc in lattice qcd
W. Kamleh and M. J. Peardon · 2006
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Recent computational developments in Krylov subspace methods for linear systems
V. Simoncini and Daniel B. Szyld · 2007
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Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part I: Seeking one eigenvalue
Andreas Stathopoulos · 2007
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Large-scale topology optimization using preconditioned krylov subspace methods with recycling
S. Wang, E. de Sturler, and G. H. Paulino · 2007
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