Abstract: A pre-processing method and pre-processor decompose a first problem belong to a class of linear algebra problems comprising an input sparse symmetric matrix into a suite of sub-problems. The pre-processor generates a suite of signals representing the information content of a permutation of the rows and columns of the sparse symmetric matrix. These signals are used to define a block-bordered diagonal form leading to a sparse Schur-complement resolution wherein each sub-problem corresponds to a perfect parallelism in the first problem. The preprocessor allocates the sub-problems to sub-processors in a network of parallel architecture computers. The sub-processors solve the sub-problems concurrently and combine the results in a front-end computer, which outputs a solution to the first problem.

Abstract: A pre-processing method and pre-processor decomposed a first problem belong to a class of linear algebra problems comprising an input sparse symmetric matrix into a suite of sub-problems. The pro-processor generates a suite of signals representing the information content of a permutation of the rows and columns of fire sparse symmetric matrix. These signals are used to define a block-bordered block-diagonal form leading to a Schur-complement resolution wherein each sub-problem corresponds to a perfect parallelism in the first problem. The preprocessor allocates the sub-problems to sub-processors in a network of parallel architecture computers. The sub-processors solve the sub-problems concurrently and combine the results in a front-end computer, which outputs a solution to the first problem.