LAPACK: a portable linear algebra library for supercomputers

A portable FORTRAN linear algebra library, LAPACK for efficient use on a variety of high-performance computers is discussed. The library is based on the widely used LINPACK and EISPACK packages for linear equation solving, eigenvalue problems, and linear least squares, but it 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 (like matrix-matrix multiplication) in their inner loops. These block operations can be optimized to exploit the memory hierarchy of different architectures, resulting in large speedups. Divide-and-conquer algorithms are used for a variety of eigenproblems. Algorithms which are much more accurate than their conventional counterparts for a variety of problems are described