LAPACK: a portable linear algebra library for high-performance computers

The goal of the LAPACK project is to design and implement a portable linear algebra library for efficient use on a variety of high-performance computers. The library is based on the widely used LINPACK and EISPACK packages for solving linear equations, eigenvalue problems, and linear least-squares problems, but extends their functionality in a number of ways. The major methodology for making the algorithms run faster is to restructure them to perform block matrix operations (e.g., matrix-matrix multiplication) in their inner loops. These block operations may be optimized to exploit the memory hierarchy of a specific architecture. The LAPACK project is also working on new algorithms that yield higher relative accuracy for a variety of linear algebra problems. >

[1]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[2]  W. Kahan.  Accurate eigenvalues of a symmetric tri-diagonal matrix , 1966 .

[3]  A. Sluis.  Condition numbers and equilibration of matrices , 1969 .

[4]  W. Kahan,et al.  The Rotation of Eigenvectors by a Perturbation. III , 1970 .

[5]  Brian T. Smith,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[6]  Jack J. Dongarra,et al.  Matrix Eigensystem Routines — EISPACK Guide Extension , 1977, Lecture Notes in Computer Science.

[7]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.

[8]  Gene H. Golub,et al.  Matrix computations , 1983 .

[9]  Jack J. Dongarra,et al.  A fully parallel algorithm for the symmetric eigenvalue problem , 1985, PPSC.

[10]  Christian H. Bischof,et al.  The WY representation for products of householder matrices , 1985, PPSC.

[11]  Jack Dongarra,et al.  Linear algebra on high performance computers , 1986 .

[12]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[13]  Distribution of mathematical software via electronic mail , 1987, CACM.

[14]  Wayne R. Cowell,et al.  User's guide to Toolpack/1 (Release 2) in a Unix environment , 1987 .

[15]  Jack J. Dongarra,et al.  A portable environment for developing parallel FORTRAN programs , 1987, Parallel Comput..

[16]  D. Sorensen,et al.  LAPACK Working Note No. 2: Block reduction of matrices to condensed forms for eigenvalue computations , 1987 .

[17]  J. Barlow,et al.  Computing accurate eigensystems of scaled diagonally dominant matrices: LAPACK working note No. 7 , 1988 .

[18]  Per Stenström,et al.  Reducing Contention in Sharde-Memory Multiprocessors , 1988, Computer.

[19]  Jack J. Dongarra,et al.  An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.

[20]  C. Loan,et al.  A Storage-Efficient $WY$ Representation for Products of Householder Transformations , 1989 .

[21]  I. Duff,et al.  On the augmented system approach to sparse least-squares problems , 1989 .

[22]  Jack J. Dongarra,et al.  A set of level 3 basic linear algebra subprograms , 1990, TOMS.

[23]  K. A. Gallivan,et al.  Parallel Algorithms for Dense Linear Algebra Computations , 1990, SIAM Rev..