Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2007-05-22
2007-05-22
An, Meng-Al T. (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
10211624
ABSTRACT:
One embodiment of the present invention provides a system for solving a system of equations in fixed-point form. During operation, the system receives a representation of the equations in fixed-point form and stores the representation a computer memory. Next, the system reduces the dimension of the system of equations, when possible, by eliminating variables in the system of equations to produce a reduced system of equations. The system then performs interval intersections based on the Fixed Point theorem to reduce the size of a box containing solutions to the reduced system of equations. In a variation on this embodiment, the system additionally applies interval techniques to find solutions to the system of equations, when such solutions exist.
REFERENCES:
patent: 3789203 (1974-01-01), Catherall et al.
patent: 5293461 (1994-03-01), Grudic et al.
patent: 6574650 (2003-06-01), Aoki
E.R. Hansen, “Global Optimization Using Interval Analysis,” Marcel Dekker, Inc., New York, NY, 1992.
R.B. Kearfott, “A Fortran 90 Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization,” ACM Transactions on Mathematical Software, vol. 21, No. 1, Mar. 1995, pp. 63-78 http://interval.louisiana.edu/preprints.html.
R. B. Kearfott, Algorithm 763: Interval Arithmetic: A Fortran 90 Module for an Interval Data Type, ACM Trans. Math. Software, 22, vol. 4, 1996, pp. 385-392. http://interval.louisiana.edu/preprints.html.
R. B. Kearfott and M. Novoa III, “Algorithm 681: INTBIS, A portable interval Newton/bisection package”, ACM Trans. Math Software, vol. 16, No. 2, pp. 152-147. http://www.netlib.org/toms/681.
R. B. Kearfott, M. Dawande, K.S. Du, and C. Hu, “Algorithm 77: INTLIB: A Portable Fortran 77 Interval Standard Function Library,” ACM Trans. Math. Software, 20, vol. 4, Dec. 1994, pp. 447-458.
R. B. Kearfott and G.W. Walster, “On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms,” ACM Trans. Math. Software, 26, vol. 3, Sep. 2000, pp. 323-351. The publication itself says Received: Jul. 1999; revised: Mar. 2000; accepted: Mar. 2000. http://interval.louisiana.edu/preprints.html.
R.E. Moore and S.T. Jones “Safe Starting Regions for Iterative Methods”, SIAM Journal on Numerical Analysis, vol. 14, No. 6 (Dec. 1977), pp. 1051-1065.
A. Neumaier, “The Enclosure of Solutions of Parameter-Dependent Systems of Euqations,” Cambridge University Press, Cambridge, 1990, ISBN: 0-12-505630-3, Reliability in Computing pp. 269-286.
S.M. Rump, “Verification Methods for Dense and Sparse Systems of Equations,” in Topics in Validated Computations: Proceedings of the IMACS-GAMM International Workshop on Validated Computations, University of Oldenburg, J. Herzberger, ed., Elsevier Studies in Computational Mathematics, Elsevier, 1994, pp. 63-136.
Pascal Van Hentenryck, Vijay Saraswat and Yves Deville, “Design, Implementation, and Evaluation of the Constraint Language cc (FD),” Elsevier Science, Inc., 1998.
Moore Ramon E.
Walster G. William
An Meng-Al T.
Do Chat C.
Park Vaughan & Fleming LLP
Sun Microsystems Inc.
LandOfFree
Method and apparatus for solving systems of equations in... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method and apparatus for solving systems of equations in..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method and apparatus for solving systems of equations in... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3752304