An algorithm for computing minimal Geršgorin sets

作者: Vladimir R. Kostić , Agnieszka Międlar , Ljiljana Cvetković

DOI: 10.1002/NLA.2024

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摘要: Summary The existing algorithms for computing the minimal Gersgorin set are designed small and medium size (irreducible) matrices based on Perron root computations coupled with bisection method sampling techniques. Here, we first discuss drawbacks of methods present a new approach modified Newton's to find zeros parameter dependent left-most eigenvalue Z-matrix special curve tracing procedure. The advantages presented several test examples that arise in practical applications. Copyright © 2015 John Wiley & Sons, Ltd.

参考文章(14)
Lloyd N. Trefethen, Mark Embree, Spectra and Pseudospectra Princeton University Press. ,(2005) , 10.1515/9780691213101
Lloyd N. Trefethen, Spectra and pseudospectra ,(2005)
Robert J. Plemmons, Abraham Berman, Nonnegative Matrices in the Mathematical Sciences ,(1979)
Richard S. Varga, Geršgorin and his circles ,(2004)
Jorge Fabrega, Pablo Paredes, Social Contagion and Cascade Behaviors on Twitter Information-an International Interdisciplinary Journal. ,vol. 4, pp. 171- 181 ,(2013) , 10.3390/INFO4020171
Charles A. Desoer, M. Vidyasagar, Feedback Systems: Input-output Properties ,(1975)
P. Lancaster, On eigenvalues of matrices dependent on a parameter Numerische Mathematik. ,vol. 6, pp. 377- 387 ,(1964) , 10.1007/BF01386087
Ljiljana Cvetković, Vladimir Kostić, Rafael Bru, Francisco Pedroche, A simple generalization of Geršgorin’s theorem Advances in Computational Mathematics. ,vol. 35, pp. 271- 280 ,(2011) , 10.1007/S10444-009-9143-6
Olga Taussky, Bounds for characteristic roots of matrices Duke Mathematical Journal. ,vol. 15, pp. 1043- 1044 ,(1948) , 10.1215/S0012-7094-48-01593-2
V. Kostić, On general principles of eigenvalue localizations via diagonal dominance Advances in Computational Mathematics. ,vol. 41, pp. 55- 75 ,(2015) , 10.1007/S10444-014-9349-0