PCR algorithm for parallel computing minimum-norm (T) least-squares (S) solution of inconsistent linear equations

This paper presents a new highly parallel algorithm for computing the minimum-norm (T) least-squares (S) solution of inconsistent linear equations Ax=b([email protected]?R^m^x^n"r,[email protected]?R(A)). By this algorithm the solution x=A"S","T^+b is obtained in T=(1+m)(1+log"2m)+n(6+log"2(n-r+1)+log"2m+log"2n)-r(1+log"2n) steps with P=mn processors when m>=2(n-1) and with P=2n(n-1) processors otherwise.

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