Successive matrix squaring algorithm for parallel computing the weighted generalized inverse A(MN)(+)

We derive a successive;matrix squaring (SMS) algorithm to approximate the w eighted generalized inverse, which can be expressed in the form of successi ve squaring of a composite matrix T. Given an m by n matrix A with m approx imate to n, we show that the weighted generalized inverse of A can be compu ted in parallel time ranging from O(log n) to O(log(2) n) provided that the re are enough processors to support matrix multiplication in time O(log n). (C) 2000 Elsevier Science Inc. All rights reserved.