Implementing linear algebra algorithms for dense matrices on a vector pipeline machine.

*(English)*Zbl 0539.65009The basic structural features of the implementation of linear algebra algorithms are considered to achieve execution speed at supervector performance level by using a computer that is ”Cray-like” in structure. The advanced concepts like pipelining, chaining, overlapping, chime and the segmentation with additional looping structure are employed to characterize the process of restructuring of the three basic generic linear algebra algorithms: Two forms of the matrix-vector multiplication, six forms of the matrix-matrix multiplication and six forms of the solution of linear equations using Gaussian elimination, which include two variants of the Crout algorithm of Gaussian elimination, are presented. The possible memory bank conflicts are considered. The implementation is focused on algorithms written in Fortran and in a pseudovector assembly language (PVAL). Three column variants of the generic Gaussian elimination in FORTRAN 77, PVAL code and PVAL code with segmentation are supplied.

Reviewer: L.Bakule

##### MSC:

65F05 | Direct numerical methods for linear systems and matrix inversion |

65F30 | Other matrix algorithms (MSC2010) |

68N25 | Theory of operating systems |

15-04 | Software, source code, etc. for problems pertaining to linear algebra |