ScaLAPACK

ScaLAPACK is an acronym for scalable linear algebra package or scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use.\parScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and the nonsymmetric eigenproblem. Prototype codes are provided for out-of-core solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, and an HPF interface to a subset of ScaLAPACK routines.\parSoftware is available in single precision real, double precision real, single precision complex, and double precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, clusters of workstations, and any system for which PVM or MPI is available.\parEach Users’ Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users’ Guide, the source code for the package, testing and timing programs, prebuilt version of the library for a number of computers, example programs, and the full set of LAPACK Working Notes.


References in zbMATH (referenced in 417 articles , 3 standard articles )

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  1. Mai, Tina; Mortari, Daniele: Theory of functional connections applied to quadratic and nonlinear programming under equality constraints (2022)
  2. Myllykoski, Mirko: Algorithm 1019: a task-based multi-shift QR/QZ algorithm with aggressive early deflation (2022)
  3. Quintanilha, Helio Jr.; Paredes, Pedro; Hanifi, Ardeshir; Theofilis, Vassilis: Transient growth analysis of hypersonic flow over an elliptic cone (2022)
  4. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Fehling, Marc; Gassmöller, Rene; Heister, Timo; Heltai, Luca; Köcher, Uwe; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Proell, Sebastian; Simon, Konrad; Turcksin, Bruno; Wells, David; Zhang, Jiaqi: The \textttdeal.II library, Version 9.3 (2021)
  5. Drmač, Zlatko: Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices (2021)
  6. Fasi, Massimiliano; Higham, Nicholas J.: Generating extreme-scale matrices with specified singular values or condition number (2021)
  7. Lin, Lin; Wu, Xiaojie: Numerical solution of large scale Hartree-Fock-Bogoliubov equations (2021)
  8. Ming, Liangjie; Zhang, Yunong; Guo, Jinjin; Liu, Xiao; Li, Zhonghua: New models for solving time-varying LU decomposition by using ZNN method and ZeaD formulas (2021)
  9. Ozaki, Katsuhisa; Terao, Takeshi; Ogita, Takeshi; Katagiri, Takahiro: Verified numerical computations for large-scale linear systems. (2021)
  10. Pan, Shaowu; Arnold-Medabalimi, Nicholas; Duraisamy, Karthik: Sparsity-promoting algorithms for the discovery of informative Koopman-invariant subspaces (2021)
  11. Singh, Navjot; Ma, Linjian; Yang, Hongru; Solomonik, Edgar: Comparison of accuracy and scalability of Gauss-Newton and alternating least squares for CANDECOMC/PARAFAC decomposition (2021)
  12. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Clevenger, Thomas C.; Fehling, Marc; Grayver, Alexander V.; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Rastak, Reza; Tomas, Ignacio; Turcksin, Bruno; Wang, Zhuoran; Wells, David: The deal.II library, version 9.2 (2020)
  13. Hoshi, Takeo; Ogita, Takeshi; Ozaki, Katsuhisa; Terao, Takeshi: An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations (2020)
  14. Keyes, D. E.; Ltaief, H.; Turkiyyah, G.: Hierarchical algorithms on hierarchical architectures (2020)
  15. Marques, Osni; Demmel, James; Vasconcelos, Paulo B.: Bidiagonal SVD computation via an associated tridiagonal eigenproblem (2020)
  16. Popovici, Doru Thom; Schatz, Martin D.; Franchetti, Franz; Low, Tze Meng: A flexible framework for multidimensional DFTs (2020)
  17. Reguly, István Z.; Mudalige, Gihan R.: Productivity, performance, and portability for computational fluid dynamics applications (2020)
  18. Seyoon Ko, Hua Zhou, Jin Zhou, Joong-Ho Won: DistStat.jl: Towards Unified Programming for High-Performance Statistical Computing Environments in Julia (2020) arXiv
  19. Wichman, Indrek S.; Nguyen, Yen T.; Pence, Thomas J.: A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux (2020)
  20. Amestoy, Patrick R.; de la Kethulle de Ryhove, Sébastien; L’Excellent, Jean-Yves; Moreau, Gilles; Shantsev, Daniil V.: Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems (2019)

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