Recent Advances in Linear Algebra Functionality

Zbigniew Leyk

Wolfram Research

Abstract

This talk will discuss sparse-matrix algorithms implemented recently in Mathematica. We can always convert a sparse matrix to a corresponding dense matrix and use dense-matrix algorithms. But for large sparse matrices, this approach is very inefficient because most computations are performed on elements that are zero. Therefore, sparse matrices require special algorithms to solve linear equations, find eigenvalues, or compute a least squares solution. Such algorithms take into account the fact that the sparse matrices have only a few nonzero elements in each matrix row or column. Numerical examples are presented to show that the sparse-matrix algorithms are much faster than their dense-matrix counterparts.