Efficient parallel solution of linear systems
Victor Ya. Pan, John H. Reif · 1985
The most efficient known parallel algorithms for inversion of a nonsingular nxn matrix A or solving a linear system Ax=b over the rationals require O(log n) to the 2nd power time and M(n) square root of n processors (where M(n) is the number of processors required in order to multiply two nxn rational matrices in time O(log n)). Furthermore, all known polylog time algorithms for those problems are unstable: they require the calculations to be done with perfect precision; otherwise they give no results at all. This paper describes parallel algorithms that have good numerical stability and remain efficient as n grows large. Additional keywords: Iterations; Convergence; Newtons method; Computer architecture.