A systolic algorithm for the triangular Stein equation

The authors solve the Stein equation X+AXB=C, with A and B upper triangular matrices, by means of a bidimensional systolic array processor, independent of problem size. The problem is decomposed into two basic subproblems: the solution of an upper triangular system and a GAXPY operation. They obtain a size-dependent systolic algorithm by means of an appropriate chaining of the solutions of these subproblems. This systolic algorithm is transformed into a size-independent systolic array processor by using the dense-to-banded transformation