Method of and apparatus for preconditioning of a coefficient matrix of

Abstract

To analyze a physical phenomenon by a computer having a plurality of vector processors and a parallel computer, there is generated submatrices in a preconditioning for obtaining solutions of simultaneous linear equations. Nonzero elements of the coefficient matrix are stored with column number indices assigned thereto such that the elements of the coefficient matrix and the data of right-side vector are scaled according to a sum of absolute values of nondiagonal elements of the coefficient matrix and a diagonal element related thereto. The nonzero elements are sorted depending on magnitude of their absolute values to subdivide the nondiagonal nonzero elements into m submatrices E1, E2, . . . , Em each having substantially a comparable order. Using products developed between differences between a unit matrix and these submatrices in the iterative calculations for a large-sized numerical simulation, there is obtained quite a satisfactory characteristic of convergence of solutions and hence the processing speed is remarkably increased.