LAPACK

LAPACK is written in Fortran 90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision. The original goal of the LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared-memory vector and parallel processors. On these machines, LINPACK and EISPACK are inefficient because their memory access patterns disregard the multi-layered memory hierarchies of the machines, thereby spending too much time moving data instead of doing useful floating-point operations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These block operations can be optimized for each architecture to account for the memory hierarchy, and so provide a transportable way to achieve high efficiency on diverse modern machines. We use the term ”transportable” instead of ”portable” because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine. LAPACK routines are written so that as much as possible of the computation is performed by calls to the Basic Linear Algebra Subprograms (BLAS). LAPACK is designed at the outset to exploit the Level 3 BLAS — a set of specifications for Fortran subprograms that do various types of matrix multiplication and the solution of triangular systems with multiple right-hand sides. Because of the coarse granularity of the Level 3 BLAS operations, their use promotes high efficiency on many high-performance computers, particularly if specially coded implementations are provided by the manufacturer. Highly efficient machine-specific implementations of the BLAS are available for many modern high-performance computers. For details of known vendor- or ISV-provided BLAS, consult the BLAS FAQ. Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for the architecture. A Fortran 77 reference implementation of the BLAS is available from netlib; however, its use is discouraged as it will not perform as well as a specifically tuned implementation.

This software is also referenced in ORMS.


References in zbMATH (referenced in 1150 articles , 4 standard articles )

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  1. Abdelfattah, A.; Anzt, H.; Dongarra, J.; Gates, M.; Haidar, A.; Kurzak, J.; Luszczek, P.; Tomov, S.; Yamazaki, I.; YarKhan, A.: Linear algebra software for large-scale accelerated multicore computing (2016)
  2. Aruliah, D.A.; van Veen, Lennaert; Dubitski, Alex: Algorithm 956: PAMPAC: a parallel adaptive method for pseudo-arclength continuation (2016)
  3. Bai, ZhaoJun; Li, RenCang; Lin, WenWei: Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods (2016)
  4. Bestehorn, Michael: Computational Physics. With examples using Fortran. (2016)
  5. Chen, Yuxin; Keyes, David; Law, Kody J.H.; Ltaief, Hatem: Accelerated dimension-independent adaptive metropolis (2016)
  6. Diao, Huai-An; Wei, Yimin; Qiao, Sanzheng: Structured condition numbers of structured Tikhonov regularization problem and their estimations (2016)
  7. Dopico, Froilán; Uhlig, Frank: Computing matrix symmetrizers. II: New methods using eigendata and linear means; a comparison. (2016)
  8. Drmač, Zlatko; Gugercin, Serkan: A new selection operator for the discrete empirical interpolation method -- improved a priori error bound and extensions (2016)
  9. Gaudreau, P.; Slevinsky, R.; Safouhi, H.: The double exponential sinc collocation method for singular Sturm-Liouville problems (2016)
  10. Hager, William W.; Zhang, Hongchao: Projection onto a polyhedron that exploits sparsity (2016)
  11. Higham, Nicholas J.; Relton, Samuel D.: Estimating the largest elements of a matrix (2016)
  12. Jessup, Elizabeth; Motter, Pate; Norris, Boyana; Sood, Kanika: Performance-based numerical solver selection in the lighthouse framework (2016)
  13. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  14. Kiusalaas, Jaan: Numerical methods in engineering with MATLAB. (2016)
  15. Kuchta, Miroslav; Nordaas, Magne; Verschaeve, Joris C.G.; Mortensen, Mikael; Mardal, Kent-Andre: Preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains (2016)
  16. Lawrence, Piers W.; van Barel, Marc; van Dooren, Paul: Backward error analysis of polynomial eigenvalue problems solved by linearization (2016)
  17. Li, Hui; Zhang, Hongwu; Zheng, Yonggang; Zhang, Liang: A peridynamic model for the nonlinear static analysis of truss and tensegrity structures (2016)
  18. Lu, Linzhang; Wang, Teng; Kuo, Yueh-Cheng; Li, Ren-Cang; Lin, Wen-Wei: A fast algorithm for fast train palindromic quadratic eigenvalue problems (2016)
  19. Michailidis, Panagiotis D.; Margaritis, Konstantinos G.: Scientific computations on multi-core systems using different programming frameworks (2016)
  20. Napov, Artem; Li, Xiaoye S.: An algebraic multifrontal preconditioner that exploits the low-rank property. (2016)

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