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Volumn 46, Issue 3, 2008, Pages 1483-1502

Uniform convergence of a nonlinear energy-based multilevel quantization scheme

Author keywords

Centroidal voronoi tessellations; Lloyd's method; Multilevel method; Optimal quantization; Uniform convergence

Indexed keywords

CENTROIDAL VORONOI TESSELLATIONS; LLOYD'S METHOD; MULTILEVEL METHOD; OPTIMAL QUANTIZATION; UNIFORM CONVERGENCE;

EID: 55349146301     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050648699     Document Type: Article
Times cited : (12)

References (41)
  • 1
    • 84976826673 scopus 로고
    • Voronoi diagrams. A survey of a fundamental geometric data structure
    • F. AURENHAMMER, Voronoi diagrams. A survey of a fundamental geometric data structure, ACM Comput. Surveys, 23 (1990), pp. 345-405.
    • (1990) ACM Comput. Surveys , vol.23 , pp. 345-405
    • AURENHAMMER, F.1
  • 2
    • 0142014324 scopus 로고    scopus 로고
    • General highly accurate algebraic coarsening
    • A. BRANDT, General highly accurate algebraic coarsening, Electron. Trans. Numer. Anal., 10 (2000), pp. 1-20.
    • (2000) Electron. Trans. Numer. Anal , vol.10 , pp. 1-20
    • BRANDT, A.1
  • 5
    • 0142105371 scopus 로고    scopus 로고
    • Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations
    • M. CAPPELLARI AND Y. COPIN, Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations, Monthly Notices Roy. Astronom. Soc., 342 (2003), pp. 345-354.
    • (2003) Monthly Notices Roy. Astronom. Soc , vol.342 , pp. 345-354
    • CAPPELLARI, M.1    COPIN, Y.2
  • 6
    • 0036103889 scopus 로고
    • Subspace correction multilevel methods for elliptic eigenvalue problems
    • T. CHAN AND I. SHARAPOV, Subspace correction multilevel methods for elliptic eigenvalue problems, Numer. Linear Algebra Appl., 1 (1993), pp. 1-7.
    • (1993) Numer. Linear Algebra Appl , vol.1 , pp. 1-7
    • CHAN, T.1    SHARAPOV, I.2
  • 7
    • 0037249173 scopus 로고    scopus 로고
    • Efficient algebraic multigrid algorithms and their convergence
    • Q. CHANG AND Z. HUANG, Efficient algebraic multigrid algorithms and their convergence, SIAM J. Sci. Comput., 24 (2002), pp. 597-618.
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 597-618
    • CHANG, Q.1    HUANG, Z.2
  • 9
    • 33645360260 scopus 로고    scopus 로고
    • Acceleration of algorithms for the computation of centroidal Voronoi tessellations
    • Q. DU AND M. EMELIANENKO, Acceleration of algorithms for the computation of centroidal Voronoi tessellations, Numer. Linear Algebra Appl., 13 (2006), pp. 173-192.
    • (2006) Numer. Linear Algebra Appl , vol.13 , pp. 173-192
    • DU, Q.1    EMELIANENKO, M.2
  • 10
    • 55349112121 scopus 로고    scopus 로고
    • Uniform convergence of a multilevel energy-based quantization scheme
    • Notes Comput. Sci. Eng. 55, O. B. Widlund and D. E. Keyes, eds, Springer, Berlin
    • Q. DU AND M. EMELIANENKO, Uniform convergence of a multilevel energy-based quantization scheme, in Domain Decomposition Methods in Science and Engineering XVI, Lect. Notes Comput. Sci. Eng. 55, O. B. Widlund and D. E. Keyes, eds., Springer, Berlin, 2007, pp. 533-541.
    • (2007) Domain Decomposition Methods in Science and Engineering XVI, Lect , pp. 533-541
    • DU, Q.1    EMELIANENKO, M.2
  • 11
    • 33847681941 scopus 로고    scopus 로고
    • Convergence properties of the Lloyd algorithm for computing the centroidal Voronoi tessellations
    • Q. DU, M. EMELIANENKO, AND L. JU, Convergence properties of the Lloyd algorithm for computing the centroidal Voronoi tessellations, SIAM J. Numer. Anal., 44 (2006), pp. 102-119.
    • (2006) SIAM J. Numer. Anal , vol.44 , pp. 102-119
    • DU, Q.1    EMELIANENKO, M.2    JU, L.3
  • 13
    • 0033317391 scopus 로고    scopus 로고
    • Centroidal Voronoi tessellations: Applications and algorithms
    • Q. DU, V. FABER, AND M. GUNZBURGER, Centroidal Voronoi tessellations: Applications and algorithms, SIAM Rev., 41 (1999), pp. 637-676.
    • (1999) SIAM Rev , vol.41 , pp. 637-676
    • DU, Q.1    FABER, V.2    GUNZBURGER, M.3
  • 14
    • 0037114113 scopus 로고    scopus 로고
    • Grid generation and optimization based on centroidal Voronoi tessellations
    • Q. DU AND M. GUNZBURGER, Grid generation and optimization based on centroidal Voronoi tessellations, Appl. Math. Comput., 133 (2002), pp. 591-607.
    • (2002) Appl. Math. Comput , vol.133 , pp. 591-607
    • DU, Q.1    GUNZBURGER, M.2
  • 15
    • 0037127128 scopus 로고    scopus 로고
    • Meshfree, probabilistic determination of points, support spheres, and connectivities for meshless computing
    • Q. DU, M. GUNZBURGER, AND L. JU, Meshfree, probabilistic determination of points, support spheres, and connectivities for meshless computing, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 1349-1366.
    • (2002) Comput. Methods Appl. Mech. Engrg , vol.191 , pp. 1349-1366
    • DU, Q.1    GUNZBURGER, M.2    JU, L.3
  • 16
    • 0042100528 scopus 로고    scopus 로고
    • Constrained centroidal Voronoi tessellations for surfaces
    • Q. DU, M. GUNZBURGER, AND L. JU, Constrained centroidal Voronoi tessellations for surfaces, SIAM J. Sci. Comput., 24 (2003), pp. 1488-1506.
    • (2003) SIAM J. Sci. Comput , vol.24 , pp. 1488-1506
    • DU, Q.1    GUNZBURGER, M.2    JU, L.3
  • 17
    • 0037423969 scopus 로고    scopus 로고
    • Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations
    • Q. DU AND D. WANG, Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations, Internat. J. Numer. Methods Engrg., 56 (2002), pp. 1355-1373.
    • (2002) Internat. J. Numer. Methods Engrg , vol.56 , pp. 1355-1373
    • DU, Q.1    WANG, D.2
  • 18
    • 33745261230 scopus 로고    scopus 로고
    • Recent progress in robust and quality Delaunay mesh generation
    • Q. DU AND D. WANG, Recent progress in robust and quality Delaunay mesh generation, J. Comput. Appl. Math., 195 (2006), pp. 8-23.
    • (2006) J. Comput. Appl. Math , vol.195 , pp. 8-23
    • DU, Q.1    WANG, D.2
  • 19
    • 51249175171 scopus 로고
    • Higher-dimensional Voronoi diagrams in linear expected time
    • R. DWYER, Higher-dimensional Voronoi diagrams in linear expected time, Discrete Comput. Geom., 6 (1991), pp. 343-367.
    • (1991) Discrete Comput. Geom , vol.6 , pp. 343-367
    • DWYER, R.1
  • 21
    • 52449147685 scopus 로고
    • A sweepline algorithm for Voronoi diagrams
    • S. FORTUNE, A sweepline algorithm for Voronoi diagrams, Algorithmica, 2 (1987), pp. 153-174.
    • (1987) Algorithmica , vol.2 , pp. 153-174
    • FORTUNE, S.1
  • 22
    • 0025403695 scopus 로고
    • On multilevel iterative methods for optimization problems
    • E. GELMAN AND J. MANDEL, On multilevel iterative methods for optimization problems, Math. Programming, 48 (1990), pp. 1-17.
    • (1990) Math. Programming , vol.48 , pp. 1-17
    • GELMAN, E.1    MANDEL, J.2
  • 23
    • 0018491303 scopus 로고
    • Asymptotically optimal block quantization
    • A. GERSHO, Asymptotically optimal block quantization, IEEE Trans. Inform. Theory, 25 (1979), pp. 373-380.
    • (1979) IEEE Trans. Inform. Theory , vol.25 , pp. 373-380
    • GERSHO, A.1
  • 25
    • 0001654023 scopus 로고
    • Analysis of a damped nonlinear multilevel method
    • W. HACKBUSCH AND A. REUSKEN, Analysis of a damped nonlinear multilevel method, Numer. Math., 55 (1989), pp. 225-246.
    • (1989) Numer. Math , vol.55 , pp. 225-246
    • HACKBUSCH, W.1    REUSKEN, A.2
  • 26
    • 0141839118 scopus 로고    scopus 로고
    • Beyond stippling methods for distributing objects on the plane
    • S. HILLER, H. HELLWIG, AND O. OBUSSEN, Beyond stippling methods for distributing objects on the plane, Computer Graphics Forum, 22 (2003), pp. 515-522.
    • (2003) Computer Graphics Forum , vol.22 , pp. 515-522
    • HILLER, S.1    HELLWIG, H.2    OBUSSEN, O.3
  • 27
    • 0036787154 scopus 로고    scopus 로고
    • Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations
    • L. JU, Q. DU, AND M. GUNZBURGER, Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations, Parallel Comput., 28 (2002), pp. 1477-1500.
    • (2002) Parallel Comput , vol.28 , pp. 1477-1500
    • JU, L.1    DU, Q.2    GUNZBURGER, M.3
  • 28
    • 33748786274 scopus 로고    scopus 로고
    • Adaptive multiscale redistribution for vector quantization
    • Y. KOREN AND I. YAVNEH, Adaptive multiscale redistribution for vector quantization, SIAM J. Sci. Comput., 27 (2006), pp. 1573-1593.
    • (2006) SIAM J. Sci. Comput , vol.27 , pp. 1573-1593
    • KOREN, Y.1    YAVNEH, I.2
  • 29
    • 23844490564 scopus 로고    scopus 로고
    • A multigrid approach to the 1-D quantization problem
    • Y. KOREN, I. YAVNEH, AND A. SPIRA, A multigrid approach to the 1-D quantization problem, IEEE Trans. Inform. Theory, 51 (200), pp. 2993-2998.
    • IEEE Trans. Inform. Theory , vol.51 , Issue.200 , pp. 2993-2998
    • KOREN, Y.1    YAVNEH, I.2    SPIRA, A.3
  • 31
    • 0018918171 scopus 로고
    • An algorithms for vector quantizer design
    • Y. LINDE, A. BUZO, AND R. GRAY, An algorithms for vector quantizer design, IEEE Trans. Commun., 28 (1980), pp. 84-95.
    • (1980) IEEE Trans. Commun , vol.28 , pp. 84-95
    • LINDE, Y.1    BUZO, A.2    GRAY, R.3
  • 32
    • 0020102027 scopus 로고
    • Least square quantization in PCM
    • S. LLOYD, Least square quantization in PCM, IEEE Trans. Inform. Theory, 28 (1982), pp. 129-137.
    • (1982) IEEE Trans. Inform. Theory , vol.28 , pp. 129-137
    • LLOYD, S.1
  • 33
    • 84974828317 scopus 로고    scopus 로고
    • Multi-outlet retail site location assessment
    • A. MENDES AND I. THEMIDO, Multi-outlet retail site location assessment, Int. Trans. Oper. Res., 11 (2004), pp. 1-18.
    • (2004) Int. Trans. Oper. Res , vol.11 , pp. 1-18
    • MENDES, A.1    THEMIDO, I.2
  • 35
    • 55349122125 scopus 로고    scopus 로고
    • J. W. RUGE AND K. STUBEN, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., Frontiers in Appl. Math. 3, SIAM, Philadelphia, 1987, pp. 73-130.
    • J. W. RUGE AND K. STUBEN, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., Frontiers in Appl. Math. 3, SIAM, Philadelphia, 1987, pp. 73-130.
  • 36
    • 0022683355 scopus 로고
    • Global convergence and empirical consistency of the generalized Lloyd algorithm
    • J. SABIN AND R. GRAY, Global convergence and empirical consistency of the generalized Lloyd algorithm, IEEE Trans. Inform. Theory, 32 (1986), pp. 148-155.
    • (1986) IEEE Trans. Inform. Theory , vol.32 , pp. 148-155
    • SABIN, J.1    GRAY, R.2
  • 37
    • 0036003411 scopus 로고    scopus 로고
    • Global convergence of subspace correction methods for some convex optimization problems
    • X. TAI AND J. XU, Global convergence of subspace correction methods for some convex optimization problems, Math. Comp., 71 (2002), pp. 105-124.
    • (2002) Math. Comp , vol.71 , pp. 105-124
    • TAI, X.1    XU, J.2
  • 38
    • 0027878665 scopus 로고
    • On the design of an optimal quantizer
    • A. TRUSHKIN, On the design of an optimal quantizer, IEEE Trans. Inform. Theory, 39 (1993), pp. 1180-1194.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1180-1194
    • TRUSHKIN, A.1
  • 39
    • 4644343599 scopus 로고    scopus 로고
    • Approximated centroidal Voronoi diagrams for uniform polygonal mesh coarsening
    • S. VALETTE AND J. CHASSERY, Approximated centroidal Voronoi diagrams for uniform polygonal mesh coarsening, Computer Graphics Forum, 23 (2004), pp. 381-390.
    • (2004) Computer Graphics Forum , vol.23 , pp. 381-390
    • VALETTE, S.1    CHASSERY, J.2
  • 40
    • 2442455496 scopus 로고    scopus 로고
    • Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging
    • C. WAGER, B. COULL, AND N. LANGE, Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging, J. R. Stat. Soc. Ser. B Stat. Methodol., 66 (2004), pp. 429-446.
    • (2004) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.66 , pp. 429-446
    • WAGER, C.1    COULL, B.2    LANGE, N.3
  • 41
    • 0036016141 scopus 로고    scopus 로고
    • The method of alternating projections and the method of subspace corrections in Hubert space
    • J. XU AND L. ZIKATANOV, The method of alternating projections and the method of subspace corrections in Hubert space, J. Amer. Math. Soc., 15 (2002), pp. 573-597.
    • (2002) J. Amer. Math. Soc , vol.15 , pp. 573-597
    • XU, J.1    ZIKATANOV, L.2


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