GerSgorin and His Circles

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Februar 2011



"Contains numerous simple examples and illustrative diagrams....For anyone seeking information about eigenvalue inclusion theorems, this book will be a great reference." --Mathematical Reviews This book studies the original results, and their extensions, of the Russian mathematician S.A. GerSgorin who wrote a seminal paper in 1931 on how to easily obtain estimates of all n eigenvalues (characteristic values) of any given n-by-n complex matrix.


Basic Theory.- GerSgorin-Type Eigenvalue Inclusion Theorems.- More Eigenvalue Inclusion Results.- Minimal GerSgorin Sets and Their Sharpness.- G-Functions.- GerSgorin-Type Theorems for Partitioned Matrices.



From the reviews:
"This book is an extremely detailed account of eigenvalue inclusion theorems, starting with the basic GerSgorin disk theorem ... . One of the most pleasing features of the book is what Varga calls the first recurring theme: every eigenvalue inclusion theorem has a corresponding nonsingularity theorem. ... contains numerous simple examples and illustrative diagrams, and everything is explained in great detail. ... For anyone seeking information about eigenvalue inclusion theorems, this book will be a great reference." (David Scott Watkins, Mathematical Reviews, 2005h)
"The monograph presents a survey of results about spectrum localization for matrices, beginning with the first GerSgorin's eigenvalue inclusion result ... . This book contains many new and some unpublished results as a survey of many GerSgorin type results in the literature. The presented material is almost entirely self-contained with exercises which are useful both for graduate students in mathematics and physicists, engineers and computer scientists." (Boris V. Loginov, Zentralblatt MATH, 1057:8, 2005)
"The new book of Varga contains, along with several new results, nearly all that has been discovered about eiegnvalue inclusions since 1931. ... One of the merits of this book is the information that it provides about Semën Aronovic Gersgorin ... . I like this book and recommend reading it." (L. Elsner, American Mathematical Monthly, Vol. 113, April, 2006)
EAN: 9783540211006
ISBN: 3540211004
Untertitel: 'Springer Series in Computational Mathematics'. 1st ed. 2004, Corr. 4th printing 2011. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Februar 2011
Seitenanzahl: 236 Seiten
Format: gebunden
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