VLSI implementation of pipelined linear system solver

A linear rotation-based algorithm without pivoting for solving linear system equations of the form Ax=b is presented. This algorithm modifies the conventional Gaussian elimination method and avoids the problems of numerical singularity and ill conditioning. It is shown that this algorithm can be implemented with a trapezoid-type array with n²/2+(n-2) processors, and a linear array with n processors, where n is the rank of this linear system. The former array performs the triangularization of matrix A using the modified linear rotation algorithm, and the latter array carries out the backward substitution for evaluating the solution of x. The computing time for solving linear system equations will be O(5n) time units. The architecture is simple, uniform, and regular, so it is well suited for implementation in VLSI