Transformation of Matrices into Banded Form

A class of full or triangular matrices R is described for which there exist banded matrices 13 such that the product BR is also banded. The banded matrices yield recursion relations for solving systems of linear equations. Examples of such matrices (arising from second derivative operators acting on orthogonal function expansions) are used to illustrate the main theorem and its application. Practical considerations in efficient implementation arc discussed. ‘T 1989 Academic Press, Inc. 1