Parallel processing computer for solving dense systems of linear equations by factoring rows, columns, and diagonal, inverting the diagonal, forward eliminating, and back substituting

摘要

A parallel processing computer system for solving a system of linear equations having coefficients residing in a first matrix and right- hand sides of the linear equations residing in a first vector. The first matrix is divided into a plurality of ND row disk sections, a plurality of ND column disk sections and ND diagonal disk sections. Each of these sections, in a preferred embodiment, are known as disk sections, and are stored on non-volatile media such as magnetic and/or optical disks. Further, the equations are defined by the first vector, the first vector comprising ND sections. Each of the plurality of j row sections and j column sections is factored. Then, the j diagonal section is factored and inverted. In a preferred embodiment, the inversion uses a Gauss-Jordan technique. These steps are repeated for all values of j that range between 1 and ND. Then, forward elimination is performed for all sections in the first vector using the first matrix, and back substitution is performed for all sections in the first vector using the first matrix.