메뉴 건너뛰기




Volumn 21, Issue 1, 1995, Pages 63-78

A Fortran 90 Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization

Author keywords

automatic differentiation; Fortran 90; global optimization; nonlinear algebraic systems; symbolic computation

Indexed keywords

AUTOMATIC DIFFERENTIATION; BACKWARD MODES; CONDITIONAL BRANCHES; DERIVATIVE INFORMATIONS; DESIGN PRINCIPLES; DYNAMIC DATA STRUCTURES; EXHAUSTIVE SEARCH ALGORITHMS; FORTRAN 90; INEQUALITY CONSTRAINTS; INTERNAL REPRESENTATIONS; INTERVAL COMPUTATIONS; INTERVAL DATUM; NON-LINEAR OPTIMIZATIONS; NONLINEAR ALGEBRAIC SYSTEMS; OPERATOR OVERLOADING; PRODUCTION WORKS; PROTOTYPING; SYMBOLIC COMPUTATION; SYSTEMS OF EQUATIONS;

EID: 0002089855     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/200979.200991     Document Type: Article
Times cited : (23)

References (40)
  • 2
    • 0023564433 scopus 로고
    • Fortran-SC-A study of a Fortran extension for engineering scientific computation with access to ACRITH
    • BLEHER, J. H., RUMP, S. M., KULISCH, U., METZGER, M., ULLRICH, C., AND WALTER, W. 1987. Fortran-SC-A study of a Fortran extension for engineering scientific computation with access to ACRITH. Computing 39, 2, 93-110.
    • (1987) Computing , vol.39 , Issue.2 , pp. 93-110
    • BLEHER, J.H.1    RUMP, S.M.2    KULISCH, U.3    METZGER, M.4    ULLRICH, C.5    WALTER, W.6
  • 4
    • 0026862533 scopus 로고
    • Reverse accumulation and accurate rounding error estimates for Taylor series coefficients
    • CHRISTIANSON, B. 1992. Reverse accumulation and accurate rounding error estimates for Taylor series coefficients. Optim. Meth. Softw. 1, 1, 81-94.
    • (1992) Optim. Meth. Softw. , vol.1 , Issue.1 , pp. 81-94
    • CHRISTIANSON, B.1
  • 5
    • 1542692661 scopus 로고
    • Tech. Rep. 1470, Mathematics Research Center, Univ. of Wisconsin, Madison
    • CRARY, F. 1976. The AUGMENT precompiler. Tech. Rep. 1470, Mathematics Research Center, Univ. of Wisconsin, Madison.
    • (1976) The AUGMENT precompiler
    • CRARY, F.1
  • 6
    • 2442750739 scopus 로고
    • Automatic differentiation of large sparse systems
    • DIXON, L. C. W., MAANY, Z., AND MOHSENINIA, M. 1990. Automatic differentiation of large sparse systems. J. Econ. Dyn. Control 14, 299-311.
    • (1990) J. Econ. Dyn. Control , vol.14 , pp. 299-311
    • DIXON, L.C.W.1    MAANY, Z.2    MOHSENINIA, M.3
  • 9
    • 0037617007 scopus 로고
    • The chain rule revisited in scientific computing
    • a
    • GRIEWANK, A. 1991a. The chain rule revisited in scientific computing. SIAM News 24, 3, 20-21.
    • (1991) SIAM News , vol.24 , Issue.3 , pp. 20-21
    • GRIEWANK, A.1
  • 10
    • 0037617007 scopus 로고
    • The chain rule revisited in scientific computing
    • b
    • GRIEWANK, A. 1991b. The chain rule revisited in scientific computing. SIAM News 24, 4, 8-24.
    • (1991) SIAM News , vol.24 , Issue.4 , pp. 8-24
    • GRIEWANK, A.1
  • 12
    • 2942676778 scopus 로고
    • Solving large systems of nonlinear constraints with application to data modeling
    • HAGER, G. D. 1993. Solving large systems of nonlinear constraints with application to data modeling. Interval Comput., 2, 169-200.
    • (1993) Interval Comput , vol.2 , pp. 169-200
    • HAGER, G.D.1
  • 13
    • 84946964686 scopus 로고
    • Interval-based techniques for sensor data fusion
    • Prepr. GRASP Lab, Univ. of Pennsylvania, Philadelphia, Pa
    • HAGER, G. 1990. Interval-based techniques for sensor data fusion. Prepr. GRASP Lab, Univ. of Pennsylvania, Philadelphia, Pa.
    • (1990)
    • HAGER, G.1
  • 15
    • 84976770443 scopus 로고
    • Methods of fast automatic differentiation and applications. Tech. Rep. RMI 87-02, Dept. of Mathematical Engineering and Instrumentation Physics, Univ. of Tokyo, Japan
    • IRI, M. AND KUBOTA, K. 1987. Methods of fast automatic differentiation and applications. Tech. Rep. RMI 87-02, Dept. of Mathematical Engineering and Instrumentation Physics, Univ. of Tokyo, Japan.
    • (1987)
    • IRI, M.1    KUBOTA, K.2
  • 17
    • 0012315827 scopus 로고
    • An interval branch and bound algorithm for bound constrained optimization problems
    • KEARFOTT, R. B. 1992. An interval branch and bound algorithm for bound constrained optimization problems. J. Global Optim. 2, 259-280.
    • (1992) J. Global Optim. , vol.2 , pp. 259-280
    • KEARFOTT, R.B.1
  • 18
    • 0026385462 scopus 로고
    • Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems
    • KEARFOTT, R. B. 1991. Decomposition of arithmetic expressions to improve the behavior of interval iteration for nonlinear systems. Computing 47, 2, 169-191.
    • (1991) Computing , vol.47 , Issue.2 , pp. 169-191
    • KEARFOTT, R.B.1
  • 19
    • 6144291755 scopus 로고
    • Interval Newton/generalized bisection when there are singularities near roots
    • a
    • KEARFOTT, R. B. 1990a. Interval Newton/generalized bisection when there are singularities near roots. Ann. Oper. Res. 25, 1, 181-196.
    • (1990) Ann. Oper. Res. , vol.25 , Issue.1 , pp. 181-196
    • KEARFOTT, R.B.1
  • 20
    • 0025445385 scopus 로고
    • Preconditioners for the interval Gauss-Seidel method
    • b, (June)
    • KEARFOTT, R. B. 1990b. Preconditioners for the interval Gauss-Seidel method. SIAM J. Numer. Anal. 27, 3 (June), 804-822.
    • (1990) SIAM J. Numer. Anal. , vol.27 , Issue.3 , pp. 804-822
    • KEARFOTT, R.B.1
  • 21
    • 84966261060 scopus 로고
    • Abstract generalized bisection and a cost bound
    • (July)
    • KEARFOTT, R. B. 1987. Abstract generalized bisection and a cost bound. Math. Comput. 49, 179 (July), 187-202.
    • (1987) Math. Comput. , vol.49 , Issue.179 , pp. 187-202
    • KEARFOTT, R.B.1
  • 22
    • 62549136247 scopus 로고
    • The cluster problem in multivariate global optimization
    • Preprint, Dept. of Mathematics, Univ. of Southwestern Louisiana, Lafayette, La
    • KEARFOTT, R. B. AND DU, K. 1992. The cluster problem in multivariate global optimization. Preprint, Dept. of Mathematics, Univ. of Southwestern Louisiana, Lafayette, La.
    • (1992)
    • KEARFOTT, R.B.1    DU, K.2
  • 23
    • 0025446701 scopus 로고
    • INTBIS, a portable interval Newton/bisection package (Algorithm 681)
    • KEARFOTT, R. B. AND NOVOA, M. 1990. INTBIS, a portable interval Newton/bisection package (Algorithm 681). ACM Trans. Math. Softw. 16, 2, 152-157.
    • (1990) ACM Trans. Math. Softw. , vol.16 , Issue.2 , pp. 152-157
    • KEARFOTT, R.B.1    NOVOA, M.2
  • 24
    • 62549150472 scopus 로고
    • A preconditioner selection heuristic for efficient iteration with decomposition of arithmetic expressions for nonlinear systems
    • KEARFOTT, R. B. AND SHI, X. 1993. A preconditioner selection heuristic for efficient iteration with decomposition of arithmetic expressions for nonlinear systems. Interval Comput., 1, 15-33.
    • (1993) Interval Comput , vol.1 , pp. 15-33
    • KEARFOTT, R.B.1    SHI, X.2
  • 25
    • 6144284223 scopus 로고
    • Rigorous computation of surface patch intersection curves
    • Preprint. Dept. of Mathematics, Univ. of Southwestern Louisiana, Lafayette, La
    • KEARFOTT, R. B. AND XING. Z. 1994. Rigorous computation of surface patch intersection curves. Preprint. Dept. of Mathematics, Univ. of Southwestern Louisiana, Lafayette, La.
    • (1994)
    • KEARFOTT, R.B.1    XING, Z.2
  • 26
    • 0028754553 scopus 로고
    • Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library
    • KEARFOTT, R. B., DAWANDE, M., DU. K.-S., AND HU, C.-Y. 1994. Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Softw. 20, 4.
    • (1994) ACM Trans. Math. Softw. , vol.20 , pp. 4
    • KEARFOTT, R.B.1    DAWANDE, M.2    DU, K.-S.3    HU, C.-Y.4
  • 27
    • 62549164429 scopus 로고
    • INTLIB: A portable Fortran-77 elementary function library
    • KEARFOTT, R. B., DAWANDE, M., Du K.-S., AND HU, C.-Y. 1992. INTLIB: A portable Fortran-77 elementary function library. Interval Comput. 3, 5.
    • (1992) Interval Comput , vol.3 , pp. 5
    • KEARFOTT, R.B.1    DAWANDE, M.2    Du, K.-S.3    HU, C.-Y.4
  • 28
    • 0010451267 scopus 로고
    • A review of preconditioners for the interval Gauss-Seidel method
    • KEARFOTT, R. B., HU, C. Y., AND NOVOA, M., III. 1991. A review of preconditioners for the interval Gauss-Seidel method. Interval Comput. 1, 1, 59-85.
    • (1991) Interval Comput , vol.1 , Issue.1 , pp. 59-85
    • KEARFOTT, R.B.1    HU, C.Y.2    NOVOA, M.3
  • 30
    • 0026874578 scopus 로고
    • An efficient method for the numerical evaluation of partial derivatives of arbitrary order
    • (June)
    • NEIDINGER, R. D. 1992. An efficient method for the numerical evaluation of partial derivatives of arbitrary order. ACM Trans. Math. Softw. 18, 2 (June), 159-173.
    • (1992) ACM Trans. Math. Softw. , vol.18 , Issue.2 , pp. 159-173
    • NEIDINGER, R.D.1
  • 32
    • 0023272008 scopus 로고
    • An introduction to the scientific computing language Pascal-SC
    • RALL, L. B. 1987. An introduction to the scientific computing language Pascal-SC. Comput. Math. Appl. 14, 1, 53-59.
    • (1987) Comput. Math. Appl. , vol.14 , Issue.1 , pp. 53-59
    • RALL, L.B.1
  • 35
    • 0026889111 scopus 로고
    • Interval analysis for computer graphics
    • (July)
    • SNYDER, J. M. 1992. Interval analysis for computer graphics. Comput. Graph. 26, 2 (July), 121-130.
    • (1992) Comput. Graph. , vol.26 , Issue.2 , pp. 121-130
    • SNYDER, J.M.1
  • 36
    • 0042112078 scopus 로고
    • Test results for a global optimization algorithm
    • 1984
    • WALSTER, G. W., HANSEN, E. R., AND SENGUPTA, S. 1985. Test results for a global optimization algorithm. In Numerical Optimization 1984, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, Eds. SIAM Philadelphia, Pa., 272-287.
    • (1985) Numerical Optimization , pp. 272-287
    • WALSTER, G.W.1    HANSEN, E.R.2    SENGUPTA, S.3
  • 37
    • 0348147109 scopus 로고
    • FORTRAN-XSC: A portable Fortran 90 module library for accurate and reliable scientific computing
    • a
    • WALTER, W. V. 1993a. FORTRAN-XSC: A portable Fortran 90 module library for accurate and reliable scientific computing. Comput. Suppl. 9, 265-286.
    • (1993) Comput. Suppl. , vol.9 , pp. 265-286
    • WALTER, W.V.1
  • 38
    • 77956812331 scopus 로고
    • ACRITH-XSC: A Fortran-like language for verified scientific computing
    • b, E. Adams and U. Kulish, Eds., Academic Press, New York.
    • WALTER, W. V. 1993b. ACRITH-XSC: A Fortran-like language for verified scientific computing. In Scientific Computing with Automatic Result Verification, E. Adams and U. Kulish, Eds., Academic Press, New York.
    • (1993) Scientific Computing with Automatic Result Verification
    • WALTER, W.V.1
  • 39
    • 0000547784 scopus 로고
    • A simple automatic derivative evaluation program
    • (Aug.)
    • WENGERT, R. E. 1964. A simple automatic derivative evaluation program. Commun. ACM 7, 8 (Aug.), 463-464.
    • (1964) Commun. ACM , vol.7 , Issue.8 , pp. 463-464
    • WENGERT, R.E.1
  • 40
    • 0018440313 scopus 로고
    • Software for interval arithmetic: A reasonably portable package
    • YOHE, J. M. 1979. Software for interval arithmetic: A reasonably portable package. ACM Trans. Math. Softw. 5, 1, 50-53.
    • (1979) ACM Trans. Math. Softw. , vol.5 , Issue.1 , pp. 50-53
    • YOHE, J.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.