ScaLAPACK's MRRR algorithm
暂无分享,去创建一个
[1] Yousef Saad,et al. Numerical Methods for Electronic Structure Calculations of Materials , 2010, SIAM Rev..
[2] James Demmel,et al. Practical experience in the numerical dangers of heterogeneous computing , 1997, TOMS.
[3] Jack Dongarra,et al. LAPACK Working Note 37: Two Dimensional Basic Linear Algebra Communication Subprograms , 1991 .
[4] Inderjit S. Dhillon,et al. Glued Matrices and the MRRR Algorithm , 2005, SIAM J. Sci. Comput..
[5] James Demmel,et al. Accurate Singular Values of Bidiagonal Matrices , 1990, SIAM J. Sci. Comput..
[6] Elena Breitmoser,et al. A performance study of the PLAPACK and ScaLAPACK Eigensolvers on HPCx for the standard problem , 2003 .
[7] Daniel Sánchez-Portal,et al. Density‐functional method for very large systems with LCAO basis sets , 1997 .
[8] Inderjit S. Dhillon,et al. Fernando's solution to Wilkinson's problem: An application of double factorization , 1997 .
[9] James Demmel,et al. Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers , 2008, SIAM J. Sci. Comput..
[10] Charles L. Lawson,et al. Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.
[11] W. Kohn,et al. Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .
[12] Wilfried N. Gansterer,et al. Computing Approximate Eigenpairs of Symmetric Block Tridiagonal Matrices , 2003, SIAM J. Sci. Comput..
[13] Gerard L. G. Sleijpen,et al. A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM Rev..
[14] William Gropp,et al. Skjellum using mpi: portable parallel programming with the message-passing interface , 1994 .
[15] Christof Vömel. LAPACK WORKING NOTE 194 : A REFINED REPRESENTATION TREE FOR MRRR , 2022 .
[16] Andrew G. Glen,et al. APPL , 2001 .
[17] J. Demmel,et al. Sun Microsystems , 1996 .
[18] B. Parlett,et al. Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices , 2004 .
[19] Beresford N. Parlett. For tridiagonals T replace T with LDL t , 2000 .
[20] Inderjit S. Dhillon,et al. Current inverse iteration software can fail , 1998 .
[21] Robert C. Ward,et al. A parallel symmetric block-tridiagonal divide-and-conquer algorithm , 2007, TOMS.
[22] Beresford N. Parlett,et al. An implementation of the dqds algorithm (positive case) , 2000 .
[23] Lin-wang Wang,et al. Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots , 1994 .
[24] Christof Vömel,et al. LAPACK WORKING NOTE 168: PDSYEVR. SCALAPACK’S PARALLEL MRRR ALGORITHM FOR THE SYMMETRIC EIGENVALUE PROBLEM , 2005 .
[25] T. Arias,et al. Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .
[26] Inderjit S. Dhillon,et al. The design and implementation of the MRRR algorithm , 2006, TOMS.
[27] J. Demmel,et al. On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic. , 1995 .
[28] Jaeyoung Choi,et al. The design of a parallel dense linear algebra software library: Reduction to Hessenberg, tridiagonal, and bidiagonal form , 1995, Numerical Algorithms.
[29] Robert A. van de Geijn,et al. Using PLAPACK - parallel linear algebra package , 1997 .
[30] R. C. Whaley,et al. Parallel and Distributed Scientific Computing , 2000, Handbook on Parallel and Distributed Processing.
[31] Ilse C. F. Ipsen. Computing an Eigenvector with Inverse Iteration , 1997, SIAM Rev..
[32] Jack J. Dongarra,et al. An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.
[33] Jack J. Dongarra,et al. A set of level 3 basic linear algebra subprograms , 1990, TOMS.
[34] Anthony Skjellum,et al. Using MPI: Portable Programming with the Message-Passing Interface , 1999 .
[35] B. Parlett. The Symmetric Eigenvalue Problem , 1981 .
[36] Y. Saad,et al. Finite-difference-pseudopotential method: Electronic structure calculations without a basis. , 1994, Physical review letters.
[37] James R. Chelikowsky,et al. Real-space pseudopotential method for computing the electronic properties of periodic systems , 2004 .
[38] Robert A. van de Geijn,et al. A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations , 2005, SIAM J. Sci. Comput..
[39] R. Ward,et al. Performance of Parallel Eigensolvers on Electronic Structure Calculations II , 2005 .
[40] Bernd G. Pfrommer,et al. Unconstrained Energy Functionals for Electronic Structure Calculations , 1998 .
[41] David E. Bernholdt,et al. High performance computational chemistry: An overview of NWChem a distributed parallel application , 2000 .
[42] Gerard L. G. Sleijpen,et al. A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems , 1996, SIAM J. Matrix Anal. Appl..
[43] Beresford N. Parlett,et al. Computations of eigenpair subsets with the MRRR algorithm , 2006, Numer. Linear Algebra Appl..
[44] P. Alpatov,et al. PLAPACK Parallel Linear Algebra Package Design Overview , 1997, ACM/IEEE SC 1997 Conference (SC'97).
[45] G. Kresse,et al. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set , 1996 .
[46] B. Parlett,et al. Relatively robust representations of symmetric tridiagonals , 2000 .
[47] I. Dhillon. Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem , 1998 .
[48] Beresford N. Parlett,et al. The Spectrum of a Glued Matrix , 2009, SIAM J. Matrix Anal. Appl..
[49] Beresford N. Parlett,et al. The New qd Algorithms , 1995, Acta Numerica.
[50] Lin-wang Wang,et al. Parallel Empirical Pseudopotential Electronic Structure Calculations for Million Atom Systems , 2000 .
[51] Ilse C. F. Ipsen. A history of inverse iteration , 1994 .
[52] Lin-wang Wang,et al. Linear combination of bulk bands method for large-scale electronic structure calculations on strained nanostructures , 1999 .
[53] James Demmel,et al. ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance , 1995, Proceedings of the 1996 ACM/IEEE Conference on Supercomputing.
[54] Inderjit S. Dhillon,et al. Orthogonal Eigenvectors and Relative Gaps , 2003, SIAM J. Matrix Anal. Appl..
[55] James Demmel,et al. Algorithm 880: A testing infrastructure for symmetric tridiagonal eigensolvers , 2008, TOMS.
[56] James Demmel,et al. The Performance of Finding Eigenvalues and Eigenvaectors of Dense Symmetric Matrices on Distributed Memory Computers , 1995, PPSC.
[57] Jaeyoung Choi,et al. A Proposal for a Set of Parallel Basic Linear Algebra Subprograms , 1995, PARA.
[58] S. SIAMJ.. A PARALLEL DIVIDE AND CONQUER ALGORITHM FOR THE SYMMETRIC EIGENVALUE PROBLEM ON DISTRIBUTED MEMORY ARCHITECTURES , 1999 .
[59] Andrew V. Knyazev,et al. Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method , 2001, SIAM J. Sci. Comput..
[60] R. C. Whaley,et al. LAPACK Working Note 94: A User''s Guide to the BLACS v1.0 , 1995 .
[61] Stanko Tomić,et al. Parallel multi-band k·p code for electronic structure of zinc blend semiconductor quantum dots , 2006 .
[62] Henri Casanova,et al. Parallel and Distributed Scientific Computing: A Numerical Linear Algebra Problem Solving Environment Designer's Perspective , 1999 .
[63] Jack Dongarra,et al. MPI: The Complete Reference , 1996 .
[64] W. Kahan,et al. The Rotation of Eigenvectors by a Perturbation. III , 1970 .