Parallel eigenvalue calculation based on multiple shift-invert Lanczos and contour integral based spectral projection method
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Chao Yang | Esmond G. Ng | Lin Lin | Christopher Haine | Hasan Metin Aktulga | E. Ng | Chao Yang | Lin Lin | H. Aktulga | Christopher Haine
[1] John B. Shoven,et al. I , Edinburgh Medical and Surgical Journal.
[2] J. Sylvester. XIX. A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares , 1852 .
[3] A. George. Nested Dissection of a Regular Finite Element Mesh , 1973 .
[4] M. Saunders,et al. Solution of Sparse Indefinite Systems of Linear Equations , 1975 .
[5] Axel Ruhe. Rational Krylov sequence methods for eigenvalue computation , 1984 .
[6] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .
[7] R. Freund,et al. QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .
[8] 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..
[9] Danny C. Sorensen,et al. Implicit Application of Polynomial Filters in a k-Step Arnoldi Method , 1992, SIAM J. Matrix Anal. Appl..
[10] Y. PÐ1Þ,et al. PARPACK: An Efficient Portable Large Scale Eigenvalue Package for Distributed Memory Parallel Architectures , 1996 .
[11] A. Stathopoulos,et al. Solution of large eigenvalue problems in electronic structure calculations , 1996 .
[12] B. Fischer. Polynomial Based Iteration Methods for Symmetric Linear Systems , 1996 .
[13] Danny C. Sorensen,et al. P_ARPACK: An Efficient Portable Large Scale Eigenvalue Package for Distributed Memory Parallel Architectures , 1996, PARA.
[14] Jack Dongarra,et al. ScaLAPACK user's guide , 1997 .
[15] G. Stewart. Afternotes goes to graduate school : lectures on advanced numerical analysis : a series of lectures on advanced numerical analysis presented at the University of Maryland at College Park and recorded after the fact , 1998 .
[16] Chao Yang,et al. ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.
[17] Vipin Kumar,et al. A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..
[18] Jack Dongarra,et al. Templates for the Solution of Algebraic Eigenvalue Problems , 2000, Software, environments, tools.
[19] Patrick Amestoy,et al. A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..
[20] David R. Bowler,et al. Parallel sparse matrix multiplication for linear scaling electronic structure calculations , 2001 .
[21] T. Sakurai,et al. A projection method for generalized eigenvalue problems , 2002 .
[22] T. Sakurai,et al. A projection method for generalized eigenvalue problems using numerical integration , 2003 .
[23] Y. Saad,et al. PARSEC – the pseudopotential algorithm for real‐space electronic structure calculations: recent advances and novel applications to nano‐structures , 2006 .
[24] Merico E. Argentati,et al. Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc , 2007, SIAM J. Sci. Comput..
[25] Michael Sternberg,et al. SIPs: Shift-and-invert parallel spectral transformations , 2007, TOMS.
[26] Andrzej Bajer. Mode-Based Frequency Response Analysis With Frequency-Dependent Material Properties , 2008 .
[27] Mitsuhisa Sato,et al. A parallel method for large sparse generalized eigenvalue problems using a GridRPC system , 2008, Future Gener. Comput. Syst..
[28] Richard B. Lehoucq,et al. Anasazi software for the numerical solution of large-scale eigenvalue problems , 2009, TOMS.
[29] Eric Polizzi,et al. A Density Matrix-based Algorithm for Solving Eigenvalue Problems , 2009, ArXiv.
[30] Andreas Stathopoulos,et al. PRIMME: preconditioned iterative multimethod eigensolver—methods and software description , 2010, TOMS.
[31] F. Chatelin. Spectral approximation of linear operators , 2011 .
[32] Yousef Saad,et al. A spectrum slicing method for the Kohn-Sham problem , 2012, Comput. Phys. Commun..
[33] Eric Polizzi,et al. FEAST fundamental framework for electronic structure calculations: Reformulation and solution of the muffin-tin problem , 2011, Comput. Phys. Commun..
[34] E Weinan,et al. Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation , 2011, J. Comput. Phys..
[35] Matt Challacombe,et al. An Optimized Sparse Approximate Matrix Multiply , 2012, ArXiv.
[36] Tetsuya Sakurai,et al. Performance comparison of parallel eigensolvers based on a contour integral method and a Lanczos method , 2013, Parallel Comput..
[37] Lukas Krämer,et al. Dissecting the FEAST algorithm for generalized eigenproblems , 2012, J. Comput. Appl. Math..
[38] Yousef Saad,et al. Approximating Spectral Densities of Large Matrices , 2013, SIAM Rev..
[39] Chao Yang,et al. Trace-Penalty Minimization for Large-Scale Eigenspace Computation , 2016, J. Sci. Comput..