... Guide¹

This work was supported in part by Cray Research, Inc., through Grant LTR DTD, by the Department of Energy, through Grant DE-FG05-87ER25048, and by the National Science Foundation, through Grant DCR-8518722, with The University of Texas at Austin.

... Young²

Center for Numerical Analysis, RLM Bldg. 13.150, University of Texas, Austin, TX 78712

... workspace.³

For the red-black ordering, the Ith entry of a permutation array P(*) indicates the position J into which the Ith unknown of the original system is being mapped, that is, if ${\bf P(I)=J}$ then unknown I is mapped into position J. The Jth entry of an inverse permutation array IP(*) indicates the position I into which the Jth unknown of the permuted system must be mapped to regain the original ordering, that is, ${\bf IP(J)=I}$.

...).⁴

A matrix has Property A if and only if it is a diagonal matrix or else there exists a rearrangement of the rows and corresponding columns of the matrix which corresponds to a red-black partitioning.

... II).⁵

An L-matrix has positive diagonal elements and nonpositive off-diagonal elements.

... one.⁶

If the row and column corresponding to diagonal entry A_i,i are to be eliminated, then the right-hand side is adjusted to $b_i \leftarrow b_i/A_{i,i}$ and $b_j \leftarrow b_j-b_i A_{i,j}$ for $j \neq i$.

... matrix.⁷

IMSL (International Mathematical and Statistical Libraries, Inc.), Sixth Floor NBC Bldg., 7500 Bellaire Blvd., Houston, TX, 77036.