DEVICE FOR RAPIDLY SOLVING A SYMMETRIC LINEAR SYSTEM ON A SUPERCOMPUTER

摘要

Abstract of the Disclosure:In order to solve a symmetric linear system givenby Au = b, where A represents a symmetric coefficientmatrix equal to a three-term sum of a diagonal matrixplus an upper triangular matrix plus a lower triangularmatrix, b represents a right-hand side vector, and urepresents a solution vector, a device calculates thesolution vector by using the right-hand side vector, thediagonal matrix, and the upper triangular matrix.Supplied with an array (JA) representing a column numberof the upper triangular matrix, a pointer arrayconstructing section (11) constructs a pointer array (JL)which points to the lower triangular matrix. Suppliedwith an array (AA) and the array (JA) which collectivelyrepresent a combination of the diagonal matrix and theupper triangular matrix, a matrix decomposing section(12) decomposes the array (AA) into an approximate matrix(M) which approximates the symmetric coefficient matrix.A first product calculating section (16) calculates afirst product vector (y) by using the array (AA), thearray (JA), a first vector (x), and the pointer array(JL). A second product calculating section (17)calculates a second product vector (y') by using theapproximate matrix (M) and the second vector (x'). Aniterative calculating section (18) carries out iterativecalculation on the array (AA), the array (JA), an array(B) representing the right-hand side vector, the firstand the second product vectors (y) and (y'). The(Abstract of the Disclosure continued)iterative calculating section (18) iteratively providesthe first and the second product calculating sections(16) and (17) with the first and the second vectors (x)and (x'), respectively. The iterative calculatingsection (18) produces the solution vector (u). Thedevice may be supplied with the lower triangular matrixinstead of the upper triangular matrix.