Device for rapidly solving a symmetric linear system on a superc

Details Device for rapidly solving a symmetric linear system on a superc Device for rapidly solving a symmetric linear system on a superc

1991-06-12

1993-04-06

Nguyen, Long T.

Boots, shoes, and leggings

G06F 738

Patent

active

052009157

ABSTRACT:
In order to solve a symmetric linear system given by AU=b, a supercomputer or vector processor calculates a solution vector u using a right-hand side vector b, a diagonal matrix, and an upper triangular matrix. Supplied with an array (JA) representing a column number of the upper triangular matrix, a pointer array constructing section (11) constructs a pointer array (JL) which points to a lower triangular matrix. Supplied with an array (AA) and the array (JA) which collectively represent a combination of the diagonal matrix and the upper triangular matrix, a matrix decomposing section (12) decomposes the array (AA) into an approximate matrix (M) which approximates a symmetric coefficient matrix A. A first product calculating section (16) calculates a first product vector (y) using the array (AA), the array (JA), a first vector (x), and the pointer array (JL). A second product calculating section (17) calculates a second product vector (y') using the approximate matrix (M) and a second vector (x'). An iterative calculating section (18) carries out iterative calculation on the array (AA), the array (JA), an array (B) representing the right-hand side vector, and the first and the second product vectors (y) and (y') to iteratively provide the first and the second product calculating sections with the first and the second vectors, respectively, and to finally produce the solution vector (u).

REFERENCES:
patent: 3621209 (1971-11-01), Businger
M. L. James et al., "Applied Numerical Methods for Digital Computation with FORTRAN and CSMP", second edition, copyright 1977 by Harper & Row, Publishers, Inc. pp. 194-199.

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