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Volumn 41, Issue 3, 2003, Pages 983-1007

A local convergence proof for the minvar algorithm for computing continuous piecewise linear approximations

Author keywords

Invertible approximation; Moving mesh; Piecewise linear; Triangulation

Indexed keywords

INEVITABLE APPROXIMATIONS; MOVING MESH; PIECEWISE LINEAR; TRIANGULATIONS;

EID: 3142721126     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902402213     Document Type: Article
Times cited : (5)

References (42)
  • 2
    • 84968502702 scopus 로고
    • 2 fits to continuous functions with adjustable nodes in one and two dimensions
    • 2 fits to continuous functions with adjustable nodes in one and two dimensions, Math. Comp., 62 (1994), pp. 645-669.
    • (1994) Math. Comp. , vol.62 , pp. 645-669
    • Baines, M.J.1
  • 3
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • A. R. BARRON, Universal approximation bounds for superpositions of a sigmoidal function, IEEE Trans. Inform. Theory, 39 (1993), pp. 930-945.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 4
    • 84966238161 scopus 로고
    • Unicity of best mean approximation by second order splines with variable knots
    • D. L. BARROW, C. K. CHUI, P. W. SMITH, AND J. D. WARD, Unicity of best mean approximation by second order splines with variable knots, Math. Comp., 32 (1978), pp. 1131-1143.
    • (1978) Math. Comp. , vol.32 , pp. 1131-1143
    • Barrow, D.L.1    Chui, C.K.2    Smith, P.W.3    Ward, J.D.4
  • 5
    • 0018768186 scopus 로고
    • Voronoi diagrams from convex hulls
    • K. Q. BROWN, Voronoi diagrams from convex hulls, Inform. Process. Lett., 9 (1979), pp. 223-228.
    • (1979) Inform. Process. Lett. , vol.9 , pp. 223-228
    • Brown, K.Q.1
  • 11
    • 0003111224 scopus 로고
    • Algorithms for the construction of data dependent triangulations
    • Chapman and Hall, London
    • N. DYN, D. LEVIN, AND S. RIPPA, Algorithms for the construction of data dependent triangulations, in Algorithms for Approximation, II, Chapman and Hall, London, 1990, pp. 185-192.
    • (1990) Algorithms for Approximation, II , pp. 185-192
    • Dyn, N.1    Levin, D.2    Rippa, S.3
  • 12
    • 0000925756 scopus 로고
    • Data dependent triangulations for piecewise linear interpolation
    • N. DYN, D. LEVIN, AND S. RIPPA, Data dependent triangulations for piecewise linear interpolation, IMA J. Numer. Anal., 10 (1990), pp. 137-154.
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 137-154
    • Dyn, N.1    Levin, D.2    Rippa, S.3
  • 14
    • 0000670028 scopus 로고    scopus 로고
    • Incremental topological flipping works for regular triangulations
    • H. EDELSBRUNNER AND N. SHAH, Incremental topological flipping works for regular triangulations, Algorithmica, 15 (1996), pp. 223-241.
    • (1996) Algorithmica , vol.15 , pp. 223-241
    • Edelsbrunner, H.1    Shah, N.2
  • 15
    • 0000964441 scopus 로고    scopus 로고
    • Probability density function learning by unsupervised neurons
    • S. FIORI, Probability density function learning by unsupervised neurons, Internat. J. Neural Systems, (2001), pp. 399-417.
    • (2001) Internat. J. Neural Systems , pp. 399-417
    • Fiori, S.1
  • 16
    • 0002432565 scopus 로고
    • Multivariate adaptive regression splines
    • J. H. FRIEDMAN, Multivariate adaptive regression splines, Ann. Statist., 19 (1991), pp. 1-141.
    • (1991) Ann. Statist. , vol.19 , pp. 1-141
    • Friedman, J.H.1
  • 18
    • 0030353607 scopus 로고    scopus 로고
    • 1-approximation via an algorithm
    • 1-approximation via an algorithm, Math. Comp., 65 (1996), pp. 647-660.
    • (1996) Math. Comp. , vol.65 , pp. 647-660
    • Gayle, R.C.1    Wolfe, J.M.2
  • 19
  • 20
    • 24444474914 scopus 로고    scopus 로고
    • A local convergence proof for the minvar algorithm for computing continuous piecewise linear approximations
    • University of Michigan, Ann Arbor, MI
    • R. E. GROFF, P. P. KHARGONEKAR, AND D. E. KODITSCHEK, A Local Convergence Proof for the Minvar Algorithm for Computing Continuous Piecewise Linear Approximations, Technical report CSE-TR-464-02, University of Michigan, Ann Arbor, MI, 2002.
    • (2002) Technical Report , vol.CSE-TR-464-02
    • Groff, R.E.1    Khargonekar, P.P.2    Koditschek, D.E.3
  • 24
    • 3142700746 scopus 로고    scopus 로고
    • Generalized model formulation technique for error synthesis and error compensation on machine tools
    • Society of Manufacturing Engineers, Atlanta, GA
    • N. HAI, J. NI, AND J. YUAN, Generalized model formulation technique for error synthesis and error compensation on machine tools, in Proceedings of the NAMRX XXVI Conference, Society of Manufacturing Engineers, Atlanta, GA, 1998.
    • (1998) Proceedings of the NAMRX XXVI Conference
    • Hai, N.1    Ni, J.2    Yuan, J.3
  • 25
    • 0038891870 scopus 로고
    • Optimal segmented approximations
    • J. B. KIOUSTELIDIS, Optimal segmented approximations, Computing, 24 (1980), pp. 1-8.
    • (1980) Computing , vol.24 , pp. 1-8
    • Kioustelidis, J.B.1
  • 26
  • 27
    • 38249017477 scopus 로고
    • Robot navigation functions on manifolds with boundary
    • D. E. KODITSCHEK AND E. RIMON, Robot navigation functions on manifolds with boundary, Adv. in Appl. Math., 11 (1990), pp. 412-442.
    • (1990) Adv. in Appl. Math. , vol.11 , pp. 412-442
    • Koditschek, D.E.1    Rimon, E.2
  • 28
    • 0023015266 scopus 로고
    • Properties of n-dimensional triangulations
    • C. L. LAWSON, Properties of n-dimensional triangulations, Comput. Aided Geom. Design, 3 (1986), pp. 231-246.
    • (1986) Comput. Aided Geom. Design , vol.3 , pp. 231-246
    • Lawson, C.L.1
  • 32
    • 84966201048 scopus 로고
    • The construction of analytic diffeomorphisms for exact robot navigation on star worlds
    • E. RIMON AND D. E. KODITSCHEK, The construction of analytic diffeomorphisms for exact robot navigation on star worlds, Trans. Amer. Math. Soc., 327 (1991), pp. 71-115.
    • (1991) Trans. Amer. Math. Soc. , vol.327 , pp. 71-115
    • Rimon, E.1    Koditschek, D.E.2
  • 33
    • 0026938332 scopus 로고
    • Exact robot navigation using artificial potential fields
    • E. RIMON AND D. E. KODITSCHEK, Exact robot navigation using artificial potential fields, IEEE Trans. Rob. Autom., 8 (1992), pp. 501-518.
    • (1992) IEEE Trans. Rob. Autom. , vol.8 , pp. 501-518
    • Rimon, E.1    Koditschek, D.E.2
  • 34
    • 0000755620 scopus 로고    scopus 로고
    • Approximating the stance map of a 2 dof monoped runner
    • W. J. SCHWIND AND D. E. KODITSCHEK, Approximating the stance map of a 2 dof monoped runner, J. Nonlinear Sci., 10 (2000), pp. 533-568.
    • (2000) J. Nonlinear Sci. , vol.10 , pp. 533-568
    • Schwind, W.J.1    Koditschek, D.E.2
  • 38
    • 0031484203 scopus 로고    scopus 로고
    • Polynomial splines and their tensor products in extended linear modeling
    • C. J. STONE, M. H. HANSEN, C. KOOPERBERG, AND Y. K. TRUONG, Polynomial splines and their tensor products in extended linear modeling, Ann. Statist., 25 (1997), pp. 1371-1470.
    • (1997) Ann. Statist. , vol.25 , pp. 1371-1470
    • Stone, C.J.1    Hansen, M.H.2    Kooperberg, C.3    Truong, Y.K.4
  • 39
    • 0031518014 scopus 로고    scopus 로고
    • 2 approximation by discontinuous piecewise polynomials
    • 2 approximation by discontinuous piecewise polynomials, Math. Comp., 66 (1997), pp. 623-650.
    • (1997) Math. Comp. , vol.66 , pp. 623-650
    • Tourigny, Y.1    Saines, M.J.2
  • 40
    • 0000816388 scopus 로고    scopus 로고
    • A new moving mesh algorithm for the finite element solution of variational problems
    • Y. TOURIGNY AND F. HÜLSEMANN, A new moving mesh algorithm for the finite element solution of variational problems, SIAM J. Numer. Anal., 35 (1998), pp. 1416-1438.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1416-1438
    • Tourigny, Y.1    Hülsemann, F.2
  • 41
    • 0004145937 scopus 로고
    • Oxford University Press, New York
    • R. WEBSTER, Convexity, Oxford University Press, New York, 1994.
    • (1994) Convexity
    • Webster, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.