ST-HEC : Reliable and Scalable Software for Linear Algebra Computations on High End Computers
暂无分享,去创建一个
[1] Nicholas J. Higham,et al. INVERSE PROBLEMS NEWSLETTER , 1991 .
[2] N. Higham. Analysis of the Cholesky Decomposition of a Semi-definite Matrix , 1990 .
[3] Shivkumar Chandrasekaran,et al. Fast and Stable Algorithms for Banded Plus Semiseparable Systems of Linear Equations , 2003, SIAM J. Matrix Anal. Appl..
[4] Karen S. Braman,et al. The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance , 2001, SIAM J. Matrix Anal. Appl..
[5] Paul Van Dooren,et al. Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization , 2015, SIAM J. Matrix Anal. Appl..
[6] James Demmel,et al. Cache efficient bidiagonalization using BLAS 2.5 operators , 2008, TOMS.
[7] Raf Vandebril,et al. An implicit QR algorithm for semiseparable matrices to compute the eigendecomposition of symmetric matrices. , 2003 .
[8] David S. Watkins,et al. POLYNOMIAL EIGENVALUE PROBLEMS WITH HAMILTONIAN STRUCTURE , 2002 .
[9] Volker Mehrmann,et al. Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils , 2001, SIAM J. Sci. Comput..
[10] Ivan Slapničar,et al. Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD , 2003 .
[11] Karl MEERBERGENyAbstract. Umist a Survey of the Quadratic Eigenvalue Problem Departments of Mathematics a Survey of the Quadratic Eigenvalue Problem , 2000 .
[12] Benedikt Großer. Ein paraleller und hochgenauer O(n²) Algorithmus für die bidiagonale Singulärwertzerlegung , 2001 .
[13] R. van de Geijn,et al. A look at scalable dense linear algebra libraries , 1992, Proceedings Scalable High Performance Computing Conference SHPCC-92..
[14] R. Byers. Numerical Stability and Instability in Matrix Sign Function Based Algorithms , 1986 .
[15] Michael Parks,et al. A study of algorithms to compute the matrix exponential , 1994 .
[16] Jack J. Dongarra,et al. Key Concepts for Parallel Out-of-Core LU Factorization , 1996, Parallel Comput..
[17] R. Byers,et al. The Matrix Sign Function Method and the Computation of Invariant Subspaces , 1997, SIAM J. Matrix Anal. Appl..
[18] B. Parlett,et al. Relatively robust representations of symmetric tridiagonals , 2000 .
[19] Robert H. Halstead,et al. Matrix Computations , 2011, Encyclopedia of Parallel Computing.
[20] David S. Watkins,et al. Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elast , 2002 .
[21] Froilán M. Dopico,et al. An Orthogonal High Relative Accuracy Algorithm for the Symmetric Eigenproblem , 2003, SIAM J. Matrix Anal. Appl..
[22] Fred G. Gustavson,et al. Recursion leads to automatic variable blocking for dense linear-algebra algorithms , 1997, IBM J. Res. Dev..
[23] James Demmel,et al. Design, implementation and testing of extended and mixed precision BLAS , 2000, TOMS.
[24] Inderjit S. Dhillon,et al. Fernando's solution to Wilkinson's problem: An application of double factorization , 1997 .
[25] Christian H. Bischof,et al. A framework for symmetric band reduction , 2000, TOMS.
[26] Xiaomei Yang. Rounding Errors in Algebraic Processes , 1964, Nature.
[27] Ivan Slapničar,et al. Relative Perturbation Theory for Hyperbolic Singular Value Problem , 2001 .
[28] J. Demmel,et al. Computing the Singular Value Decomposition with High Relative Accuracy , 1997 .
[29] Richard W. Vuduc,et al. Sparsity: Optimization Framework for Sparse Matrix Kernels , 2004, Int. J. High Perform. Comput. Appl..
[30] Jack Dongarra,et al. The design and implementation of the parallel out-of-core ScaLAPACK LU, QR and Cholesky factorization routines , 1997 .
[31] S. H. Cheng,et al. A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization , 1998, SIAM J. Matrix Anal. Appl..
[32] James Demmel,et al. Error bounds from extra-precise iterative refinement , 2006, TOMS.
[33] Z. Drmač,et al. A new stable bidiagonal reduction algorithm , 2005 .
[34] Sathish S. Vadhiyar,et al. Towards an Accurate Model for Collective Communications , 2001, Int. J. High Perform. Comput. Appl..
[35] D Rotman,et al. DOE Greenbook - Needs and Directions in High-Performance Computing for the Office of Science , 2002 .
[36] James Demmel,et al. Practical Experience in the Dangers of Heterogeneous Computing , 1996, PARA.
[37] John G. Lewis,et al. Accurate Symmetric Indefinite Linear Equation Solvers , 1999, SIAM J. Matrix Anal. Appl..
[38] David S. Watkins,et al. Fundamentals of matrix computations , 1991 .
[39] Richard Vuduc,et al. Automatic performance tuning of sparse matrix kernels , 2003 .
[40] Nicholas J. Higham,et al. Computing the Matrix Cosine , 2004, Numerical Algorithms.
[41] Karen S. Braman,et al. The Multishift QR Algorithm. Part II: Aggressive Early Deflation , 2001, SIAM J. Matrix Anal. Appl..
[42] R. Byers. Solving the algebraic Riccati equation with the matrix sign function , 1987 .
[43] Erik Elmroth,et al. SIAM REVIEW c ○ 2004 Society for Industrial and Applied Mathematics Vol. 46, No. 1, pp. 3–45 Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software ∗ , 2022 .
[44] James Demmel,et al. Jacobi's Method is More Accurate than QR , 1989, SIAM J. Matrix Anal. Appl..
[45] Sabine Van Huffel,et al. SLICOT—A Subroutine Library in Systems and Control Theory , 1999 .
[46] Kurt Mehlhorn,et al. Cache-Oblivious and Cache-Aware Algorithms , 2005 .
[47] Iain S. Duff,et al. Incremental Norm Estimation for Dense and Sparse Matrices , 2002 .
[48] Gareth I. Hargreaves,et al. Computing the Condition Number of Tridiagonal and Diagonal-Plus-Semiseparable Matrices in Linear Time , 2005, SIAM J. Matrix Anal. Appl..
[49] 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..
[50] Alan J. Laub,et al. On Scaling Newton's Method for Polar Decomposition and the Matrix Sign Function , 1990, 1990 American Control Conference.
[51] Jack J. Dongarra,et al. Automated empirical optimizations of software and the ATLAS project , 2001, Parallel Comput..
[52] Inderjit S. Dhillon,et al. Orthogonal Eigenvectors and Relative Gaps , 2003, SIAM J. Matrix Anal. Appl..
[53] Fred G. Gustavson,et al. A recursive formulation of Cholesky factorization of a matrix in packed storage , 2001, TOMS.
[54] R. Byers,et al. Numerische Simulation Auf Massiv Parallelen Rechnern Numerical Computation of Deeating Subspaces of Embedded Hamiltonian Pencils Preprint-reihe Des Chemnitzer Sfb 393 , 2022 .
[55] Gene H. Golub,et al. Scaling by Binormalization , 2004, Numerical Algorithms.
[56] B. Parlett,et al. Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices , 2004 .
[57] Nicholas J. Higham,et al. A Schur-Parlett Algorithm for Computing Matrix Functions , 2003, SIAM J. Matrix Anal. Appl..
[58] Zlatko Drmac,et al. New Fast and Accurate Jacobi SVD Algorithm. I , 2007, SIAM J. Matrix Anal. Appl..
[59] William E. Johnston,et al. Creating science-driven computer architecture: A new path to scientific leadership , 2002 .
[60] J. Demmel,et al. An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems , 1997 .
[61] V. Klema. LINPACK user's guide , 1980 .
[62] Matthew I. Smith,et al. A Schur Algorithm for Computing Matrix pth Roots , 2002, SIAM J. Matrix Anal. Appl..
[63] Karl Meerbergen,et al. Locking and Restarting Quadratic Eigenvalue Solvers , 2000, SIAM J. Sci. Comput..
[64] A. Laub,et al. Rational iterative methods for the matrix sign function , 1991 .
[65] I. Dhillon. Reliable Computation of the Condition Number of a Tridiagonal Matrix in O(n) Time , 1998, SIAM J. Matrix Anal. Appl..
[66] Rui Ralha,et al. One-sided reduction to bidiagonal form , 2003 .