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Successive matrix squaring algorithm for parallel computing the weighted generalized inverse A MN + . (English) Zbl 1023.65031
Summary: We derive a successive matrix squaring algorithm to approximate the weighted generalized inverse, which can be expressed in the form of successive squaring of a composite matrix T. Given an m by n matrix A with mn, we show that the weighted generalized inverse of A can be computed in parallel time ranging from O(logn) to O(log 2 n) provided that there are enough processors to support matrix multiplication in time O(logn).
MSC:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65Y05Parallel computation (numerical methods)