Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2005-12-13
2005-12-13
Chaki, Kakali (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
C708S200000
Reexamination Certificate
active
06976048
ABSTRACT:
One embodiment of the present invention provides a system that solves a problem involving an interval parameter p through an interval solution process. During operation, the system receives a representation of the problem, wherein the problem includes a number of variables x1, x2, x3, . . . xnand at least one interval parameter p. The system stores the representation in a computer memory, and then performs the interval solution process on the problem. During this interval solution process, the system splits the problem into sub-problems by splitting the interval parameter p into subintervals, and creating separate sub-problems for each subinterval. The system then performs the interval solution process on the sub-problems. By splitting the interval parameter p, the system can achieve a tighter bound on the solution set of the problem. The decision to split on any parameter p is made in exactly the same way it would be made if p were a variable of the problem. Otherwise, parameters are kept separate from problem variables.
REFERENCES:
Nicola Femia, A Robust and Fast Convergent Interval Analysis Method for the Calculation of INternally Controlled Switching Instants, Mar. 1996, IEEE, pp. 191-199.
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. 269-186.
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 Methematics, 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.
Hansen Eldon R.
Walster G. William
Chaki Kakali
Do Chat C.
Park Vaughan & Fleming LLP
Sun Microsystems Inc.
LandOfFree
Method and apparatus solving problems having interval... 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 solving problems having interval..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method and apparatus solving problems having interval... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3472065