PCR algorithm for parallel computing the solution of the general restricted linear equations (Q949303)

The author presents a parallel Cramer's rule (PCR) algorithm for the solution of a general restricted linear equation of the form \(A x = b, \quad x \in T\), where \(T\) is a subspace of \(\mathbb{C}^n\) and \(b \in AT\). By the proposed algorithm the solution \(x = A_{T,S}^{(2)} b\) is obtained in \(n(\log_2 m + \log_2 (n-s+1)+7) + \log_2 m + 1\) steps with \(P = mn\) processors when \(m \geq 2(n-1)\) and with \(P = 2n(n-1)\) processors otherwise.