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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 $m\approx n$, we show that the weighted generalized inverse of $A$ can be computed in parallel time ranging from $O(\log n)$ to $O(\log^2n)$ provided that there are enough processors to support matrix multiplication in time $O(\log n)$.

MSC:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65Y05Parallel computation (numerical methods)
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References:
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