Input randomization and automatic derivation of systolic arrays for matrix computations

Many standard matrix algorithms are diicult to implement as systolic arrays, because they involve data movement that cannot be determined a priori, resulting in high timing complexity. In the case of dense matrix inversion, Gaussian elimination (GE) with pivoting has largely been supplanted by alternative schemes, such as Givens rotations and the Gram-Schmidt method, which are costly and complex, and the simpler GE with pairwise pivoting and GE without pivoting, which can break down on \degenerate" inputs, i.e., invertible matrices with noninvertible submatrices. A new input randomization technique eeciently transforms the linear problem Ax = b into the randomized problem (VA)x = (V b), where the matrix V is chosen from a special class of random matrices. If A is nonsingular, then, with probability 1, GE without pivoting can be successfully applied to VA. As is demonstrated by an extended tuto-rial example, this simple algorithm is amenable to current-generation matrix algorithm compilers, such as UCLA's Mamacg system.