Solving very large dense systems of linear equations on a parallel processing computer

摘要

A method in a parallel processing computer 100 of 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 sections, a plurality of ND column sections and ND diagonal sections. 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 181-184. 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. The computer comprises an array of compute nodes (such as 110, 111) and I/O nodes (such as 150). Results of the stages of computation are stored on the disks, as a precaution against system malfunction IMAGE