Quadrature rule-based bounds for functions of adjacency matrices

Linear Algebra and Its Applications

Volumn 433, Issue 3, 2010, Pages 637-652

  Benzi, Michele ^a   Boito, Paola ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

Communicability; Decay bounds; Estrada index; Graphs; Lanczos algorithm; Matrix exponential; Networks; Quadrature rules; Resolvent; Sparse matrices; Subgraph centrality

Indexed keywords

DECAY BOUNDS; LANCZOS ALGORITHM; MATRIX EXPONENTIALS; QUADRATURE RULES; SPARSE MATRICES; SUBGRAPHS;

FUNCTION EVALUATION;

EID: 77953139600     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2010.03.035     Document Type: Article

References (26)

1. Bai Z., and Golub G.H. Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Ann. Numer. Math. 4 (1997) 29-38
2. Benzi M., and Golub G.H. Bounds for the entries of matrix functions with applications to preconditioning. BIT 39 (1999) 417-438
3. Benzi M., and Razouk N. Decay rates and O (n) algorithms for approximating functions of sparse matrices. Electron. Trans. Numer. Anal. 28 (2007) 16-39
4. Berman A., and Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences (1979), Academic Press, New York, NY
5. Crofts J.J., and Higham D.J. A weighted communicability measure applied to complex brain networks. J. Roy. Soc. Interface 33 (2009) 411-414
6. de la Peña J.A., Gutman I., and Rada J. Estimating the Estrada index. Linear Algebra Appl. 427 (2007) 70-76
7. Duff I.S., Erisman A.M., and Reid J.K. Direct Methods for Sparse Matrices. second ed. Monographs on Numerical Analysis (1989), Oxford Science Publications, The Clarendon Press, Oxford University Press
8. Estrada E. Characterization of 3D molecular structure. Chem. Phys. Lett. 319 (2000) 713-718
9. Estrada E., and Hatano N. Statistical-mechanical approach to subgraph centrality in complex networks. Chem. Phys. Lett. 439 (2007) 247-251
10. Estrada E., and Hatano N. Communicability in complex networks. Phys. Rev. E 77 (2008) 036111
11. Estrada E., and Hatano N. Communicability graph and community structures in complex networks. Appl. Math. Comput. 214 (2009) 500-511
12. Estrada E., and Hatano N. Returnability in complex directed networks (digraphs). Linear Algebra Appl. 430 (2009) 1886-1896
13. E. Estrada, D.J. Higham, Network Properties Revealed Through Matrix Functions, University of Strathclyde Mathematics Research Report 17, 2008.
14. Estrada E., Higham D.J., and Hatano N. Communicability and multipartite structures in complex networks at negative absolute temperatures. Phys. Rev. E 78 (2008) 026102
15. Estrada E., Higham D.J., and Hatano N. Communicability bewteenness in complex networks. Physica A 388 (2009) 764-774
16. Estrada E., and Rodríguez-Velázquez J.A. Subgraph centrality in complex networks. Phys. Rev. E 71 (2005) 056103
17. G.H. Golub, G. Meurant, Matrices, moments and quadrature, in: Numerical Analysis, 1993, D.F. Griffiths, G.A. Watson (Eds.), Pitman Research Notes in Mathematics, vol. 303, Essex, England, 1994, pp. 105-156.
18. Golub G.H., and Meurant G. Matrices. Moments and Quadrature with Applications (2010), Princeton University Press, Princeton, NJ
19. Higham N. Functions of Matrices. Theory and Computation (2008), Society for Industrial and Applied Mathematics, Philadelphia, PA
20. Higham N. The scaling and squaring method for the matrix exponential revisited. SIAM Rev. 51 (2009) 747-764
21. Meurant G. Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm. Numer. Algorithms 51 (2009) 309-318
22. G. Meurant, MMQ toolbox for Matlab, .
23. N. Razouk, Localization Phenomena in Matrix Functions: Theory and Algorithms, Ph.D. Thesis, Emory University, Atlanta, GA, 2008.
24. A. Taylor, D.J. Higham, CONTEST: Toolbox files and documentation, .
25. Taylor A., and Higham D.J. CONTEST: a controllable test matrix toolbox for MATLAB. ACM Trans. Math. Software 35 (2009) 26:1-26:17
26. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 (1998) 440-442