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2015 | 34 | 4 |

Tytuł artykułu

On the eigenvalue distribution of adjacency matrices for connected planar graphs

Autorzy

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN

Wydawca

-

Rocznik

Tom

34

Numer

4

Opis fizyczny

p.39-60,fig.,ref.

Twórcy

  • School of Economic, Political, and Policy Sciences, University of Texas at Dallas, Dallas, USA

Bibliografia

  • Adler M., van Moerbeke P., 2001. Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum. Annals of Mathematics 153: 149–189.
  • Barry R., Pace R., 1999. Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra and Its Applications 289: 41–54.
  • Box G., Jenkins G., 1976. Time series analysis: Forecasting, and control. Holden Day, San Francisco.
  • Brouwer A., Haemers W., 2012. Spectra of graphs. Springer, New York.
  • Cao D., Yuan H., 1993. Graphs characterized by the second eigenvalue. Journal of Graph Theory 17: 25–331.
  • Cao D., Yuan H., 1995. The distribution of eigenvalues of graphs. Linear Algebra and its Applications 216: 211–224.
  • Chung F., 1997. Spectral graph theory. American Mathematical Society, Providence, RI.
  • Chung F., Lu L., Vu V., 2003. Spectra of random graphs with given expected degrees. Proceedings of the National Academy of Sciences 100: 6313–6318.
  • Cressie N., 1993. Statistics for spatial data. Wiley, New York.
  • Faloutsos M., Faloutsos P., Faloutsos C., 1999. On power-law relationships of the internet topology. ACM SIGCOM Computer Communication Review 29: 251–262.
  • Farrell P., Ehsanes Saleh A., Zhang Z., 2011. Methods of moments estimation in finite mixtures. Sankhyā: The Indian Journal of Statistics 73-A, Part 2: 218–230.
  • Fefferman C., Phong D., 1980. On the asymptotic eigenvalue distribution of a pseudo-differential operation. Proceedings of the National Academy of Sciences 77: 5622–5625.
  • Golub G., van der Vorst H., 2000. Numerical progress in eigenvalue computation in the 20th century. J. of Computational and Applied Mathematics 123: 35–65.
  • Griffith D., 2000. Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra and its Applications 321: 95–112.
  • Griffith D., 2003. Spatial autocorrelation and spatial filtering: Gaining understanding through theory and scientific visualization. Springer, New York.
  • Griffith D., 2004. Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and Its Applications 388: 201–219.
  • Griffith D., Luhanga U., 2011. Approximating the inertia of the adjacency matrix of a connected planar graph that is the dual of a geographic surface partitioning. Geographical Analysis 43: 383–402.
  • Hams A., de Raedt H., 2000. Fast algorithm for finding the eigenvalue distribution of very large matrices. Physical review, E: Statistical physics, plasmas, fluids, and related interdisciplinary topics 62 (#3): 4365–4377.
  • Henson J., Reise S., Kim K., 2007. Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling 14 (2): 202–226.
  • Huffer F., Wu H., 1998. Markov chain Monte Carlo for autologistic regression models with application to the distribution of plant species. Biometrics 54: 509–524.
  • Hyndman J., Kostenko A., 2007. Minimum sample size requirements for seasonal forecasting models. Foresight 6: 12–15.
  • Khorunzhy O., Shcherbina M., Vengerovsky V., 2004. Eigenvalue distribution of large weighted random graphs. Journal of Mathematical Physics 45 (#4): 1648–1672.
  • Liu B., Bo Z., 2000. On the third largest eigenvalue of a graph. Linear Algebra and its Applications 317: 193–200.
  • Martin R., Griffith D., 1998. Fast methods for fitting one-parameter spatial models. Department of Geography, Syracuse University Syracuse, NY (unpublished paper).
  • Sylvester J., 1852. A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Philosophical Magazine Series 4, 4 (23): 138–142.
  • Tse R., 1997. An application of the ARIMA model to real estate prices in Hong Kong. Journal of Property Finance 8: 152–163.
  • Yong X., 1999. On the distribution of eigenvalues of a simple undirected graph. Linear Algebra and its Applications 295: 73–80.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

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