Autovalores do Laplaciano - Departamento de Matemática - UFMG

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Rodney Josué Biezuner 155 [GWW2] Carolyn GORDON, David L. WEBB e Scott WOLPERT, Isospectral plane domains and surfaces via Riemannian orbifolds, Inventiones Mathematicae 110 (1992), n. 1, 1–22. [Hackbusch] W. HACKBUSCH, Elliptic Differential Equations: Theory and Numerical Treatment, Springer Series in Computational Mathematics 18, Springer, 1992. [Herrman] H. HERRMANN, Beziehungen zwischen den Eigenwerten und Eigenfunktionen verschiedener Eigenwertprobleme, Math. Z. 40 (1935), 221–241. [Heuveline] Vincent HEUVELINE, On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods, Journal of Computational Physics 184 (2003), 321–337. [Horn-Johnson] Roger A. HORN e Charles R. JOHNSON, Matrix Analysis, Cambridge University Press, 1985. [Johnson] Claes JOHNSON, Numerical solutions of partial differential equations by the finite element method, Cambridge, 1987. [Jost] Jürgen JOST, Partial Differential Equations, Graduate Texts in Mathematics 214, Springer-Verlag, 2002. [Kac] M. KAC, Can one hear the shape of a drum?, American Mathematical Monthly 73 (1966), no. 4, part II, 1–23. [Kuttler-Sigillito] J. R. KUTTLER e V. G. SIGILLITO, Eigenvalues of the Laplacian in two dimensions, SIAM REVIEW 26 (1984) no. 2, 163–193. [Milnor] J. MILNOR, Eigenvalues of the Laplace operator on certain manifolds, Proceedings of the National Academy of Sciences USA 51 (1964), 542. [Pleijel] A. PLEIJEL, Remarks on Courant’s nodal line theorem, Comm. Pure Appl. Math. 9 (1956), 543–550. [Protter] M. H. PROTTER, Can one hear the shape of a drum? Revisited, SIAM REVIEW 29 (1987) no. 2, 185–197. [Rosser1] J. Barkley ROSSER, Nine point difference solutions for Poisson’s equation, Comp. Math. Appl. 1 (1975), 351–360. [Rosser2] J. Barkley ROSSER, Finite-difference solution of Poisson’s equation in rectangles of arbitrary proportions, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 28 (1977), no.2, 185–196. [Sridhar-Kudrolli] S. SRIDAR e A. KUDROLLI, Experiments on not “hearing the shape” of drums, Physical Review Letters 72 (1994), 2175–2178. [Strang] Gilbert STRANG, Linear Algebra and its Applications, 3rd Ed., Harcourt Brace Jovanovich, 1988. [Strikwerda] John C. STRIKWERDA, Finite Difference Schemes and Partial Differential Equations, 2nd Ed., SIAM, 2004. [Thomas1] J. W. THOMAS, Numerical Partial Differential Equations: Finite Difference Methods, Texts in Applied Mathematics 22, Springer, 1995.
Rodney Josué Biezuner 156 [Thomas2] J. W. THOMAS, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Texts in Applied Mathematics 33, Springer, 1999. [Uhlenbeck1] K. UHLENBECK, Eigenfunctions of Laplace operator, Bulletin of the American Mathematical Society 78 (1972), 1073–1076. [Uhlenbeck2] K. UHLENBECK, Generic properties of eigenfunctions, American Journal of Mathematics 98 (1976), 1059–1078. [Vigneras] Marie-France VIGNÉRAS, Varietés riemanniennes isospectrales et non isometriques, Annals of Mathematics 91 (1980), 21–32. [Wat1] K. WATANABE, Plane Domains Which Are Spectrally Determined, Annals of Global Analysis and Geometry 18 (2000), no. 5, 447–475. [Wat2] K. WATANABE, Plane Domains Which Are Spectrally Determined II, J. Inequal. Appl. 7 (2002), no. 1, 25–47. [Watkins] David S. WATKINS, Fundamentals of Matrix Computations, 2nd Ed., John Wiley & Sons, 2002. [Weyl] H. WEYL, Über die Asymptotische Verteilung der Eigenwerte, Nachr. Konigl. Ges. Wiss. Göttingen (1911), 110–117. [Young] David M. YOUNG, Iterative Solutions of Large Linear Systems, Academic Press, 1971. [Zelditch] S. ZELDITCH, Spectral determination of analytic bi-axisymmetric plane domains, Geometric and Functional Analysis 10 (2000), no. 3, 628–677.
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Notas de Aula Autovalores do Laplac
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Rodney Josué Biezuner 2 3 Existên
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Capítulo 1 Os Autovalores do Lapla
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Rodney Josué Biezuner 6 O método
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Rodney Josué Biezuner 8 As autofun
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Rodney Josué Biezuner 10 onde α 1
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Rodney Josué Biezuner 12 1.4 Méto
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Rodney Josué Biezuner 14 de modo q
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Rodney Josué Biezuner 16 Estes exe
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Rodney Josué Biezuner 18 1.6 Exist
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Rodney Josué Biezuner 20 pois um p
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Rodney Josué Biezuner 22 tais que
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Rodney Josué Biezuner 24 Em outras
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Rodney Josué Biezuner 26 possui um
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Rodney Josué Biezuner 28 e portant
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Rodney Josué Biezuner 30 No caso
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Rodney Josué Biezuner 32 1.8.2 Con
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Rodney Josué Biezuner 34 de modo q
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Rodney Josué Biezuner 36 Prova: A
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Rodney Josué Biezuner 38 são line
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Rodney Josué Biezuner 40 onde x0
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Rodney Josué Biezuner 42 2.1.3 Res
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Rodney Josué Biezuner 44 porque (
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Rodney Josué Biezuner 46 Neste cas
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Rodney Josué Biezuner 48 = Ukl (
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Rodney Josué Biezuner 50 A primeir
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Rodney Josué Biezuner 52 2.5 Lema.
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Rodney Josué Biezuner 54 donde Com
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Rodney Josué Biezuner 56 isso impl
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Rodney Josué Biezuner 58 enquanto
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Rodney Josué Biezuner 60 + ∆x 5
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Rodney Josué Biezuner 62 mesmo ana
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Rodney Josué Biezuner 64 Para escr
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Rodney Josué Biezuner 66 (xi, yj
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Rodney Josué Biezuner 68 8. Mostre
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Rodney Josué Biezuner 70 A norma l
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Rodney Josué Biezuner 72 De fato,
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Rodney Josué Biezuner 74 Além dis
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Rodney Josué Biezuner 76 de uma ma
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Rodney Josué Biezuner 78 donde n |
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Rodney Josué Biezuner 80 3.10 Teor
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Rodney Josué Biezuner 82 Da defini
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Rodney Josué Biezuner 84 3.6.1 Esq
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Capítulo 4 Métodos Iterativos par
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Rodney Josué Biezuner 88 4.1.2 Mé
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Rodney Josué Biezuner 90 ou seja,
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Rodney Josué Biezuner 92 4.2.1 Con
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Rodney Josué Biezuner 94 para t su
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Rodney Josué Biezuner 96 4.7 Corol
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Rodney Josué Biezuner 98 Por outro
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Rodney Josué Biezuner 100 Suponha
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Rodney Josué Biezuner 102 ou Se λ
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Page 107 and 108: Rodney Josué Biezuner 106 Reciproc
Page 109 and 110: Rodney Josué Biezuner 108 Temos ω
Page 111 and 112: Rodney Josué Biezuner 110 se ∆x
Page 113 and 114: Rodney Josué Biezuner 112 A escolh
Page 115 and 116: Rodney Josué Biezuner 114 a conver
Page 117 and 118: Rodney Josué Biezuner 116 ou e k+1
Page 119 and 120: Rodney Josué Biezuner 118 4.31 Cor
Page 121 and 122: Capítulo 5 Métodos Multigrid 5.1
Page 123 and 124: Rodney Josué Biezuner 122 6.1 Prop
Page 125 and 126: Rodney Josué Biezuner 124 é chama
Page 127 and 128: Rodney Josué Biezuner 126 como vé
Page 129 and 130: Rodney Josué Biezuner 128 No caso
Page 131 and 132: Rodney Josué Biezuner 130 Prova. C
Page 133 and 134: Rodney Josué Biezuner 132 onde é
Page 135 and 136: Rodney Josué Biezuner 134 7.3 Coro
Page 137 and 138: Rodney Josué Biezuner 136 Como seg
Page 139 and 140: Rodney Josué Biezuner 138 Prova. O
Page 141 and 142: Capítulo 8 Métodos Numéricos par
Page 143 and 144: Rodney Josué Biezuner 142 o maior
Page 145 and 146: Rodney Josué Biezuner 144 com q1
Page 147 and 148: Rodney Josué Biezuner 146 e depois
Page 149 and 150: Rodney Josué Biezuner 148 8.3.2 Im
Page 151 and 152: Rodney Josué Biezuner 150 Pode-se
Page 153 and 154: Rodney Josué Biezuner 152 Observe
Page 155: Referências Bibliográficas [Asmar
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