Efficient linear and bilinear arrays for matrix triangularisation with partial pivoting

Abstract

The paper presents two VLSI arrays for implementing Gaussian elimination with partial pivoting. The first is a bilinear array that uses 2n+1 PEs and triangularises an n*n dense matrix in n/sup 2/+n-2 time units. The second array is a switchable linear array. It uses n PEs to triangularise the n*n dense matrix in 2n/sup 2/-2n+1 time units. Both arrays use strictly local communications and employ simple processing elements (PEs). An optional buffer array can supplement either array to avoid costly inter-iteration I/O. The arrays exhibit an area-time complexity of O(n/sup 3/) which matches the algorithm's time complexity on a uniprocessor. The architectures described are much more efficient than those previously reported by the same authors. >