L. Schork and J. Gondzio
Abstract
This paper is concerned with the problem of permuting a spiked matrix
to triangular form. A spiked matrix results from changing one column
or one row in a triangular matrix. In this paper we focus on changing
one column in an upper triangular matrix.
Spiked matrices arise in updating the LU factors of a matrix after
a column change. The LU update methods of Bartels and Golub and
Forrest and Tomlin use algebraic operations to transform a spiked
matrix to triangular form. We present an LU update method which
does the transformation by permutation alone whenever this is
possible and falls back to the Forrest-Tomlin update otherwise.
Key words: sparse LU update, permutation to triangular form.