Information processing apparatus and method for solving...

Details Information processing apparatus and method for solving... Information processing apparatus and method for solving...

2005-12-14

2010-12-21

Bullock, Jr., Lewis A (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07856466

ABSTRACT:
First, calculations to solve a given set of simultaneous linear equations are performed using a conjugate gradient method and it is determined, each time the calculations are iterated, whether or not the calculations diverge. If it is determined that the calculations diverge, the initial value of a variable is set to the minimum value and calculations to solve the set of simultaneous linear equations are performed using a conjugate residual method. This allows the set of simultaneous linear equations to be solved even if it is not known whether or not its coefficient matrix is regular.

REFERENCES:
patent: 6144932 (2000-11-01), Hachiya
patent: 05-073527 (1993-03-01), None
patent: 11-242664 (1999-09-01), None
“The application of the generalized conjugate residual algorithm to accelerate the fast multipole method”, Ning Yuan et al., 2001, p. 778-781.
“Solving linear algebraic equations can be interesting”, George Forsythe, 2002, p. 313-329.
“On the Behavior of the Conjugate Residual Method for Singular Systems”, Ken Hayami, 2001, p. 1-15.
Hayami, “On the Behaviour of the Conjugate Residual Method for Singular Systems,” NII Technical Report, NII-2001-002E (2002), 15 pages.
Abe et al., “Convergence Theory of the CR Method for Linear Singular Systems,” The Japan Society for Industrial and Applied Mathematics, vol. 9, No. 1, 1999, pp. 1-13.

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