Geršgorin and his circles

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Geršgorin and his circles / Richard S. Varga

資料種別:: 図書
出版情報:: Berlin : Springer, c2004
形態:: x, 226 p. ; 24 cm
シリーズ名:: Springer series in computational mathematics ; 36 <BA0020163X>
著者名:: Varga, Richard S., 1928- <DA01346714>
ISBN:: 9783540211006 [3540211004]
書誌ID:: BA68494063

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注記:

Includes bibliographical references and index

主題:

Algebras, Linear; Eigenvalues; Geršgorin, Semen Aronovich, 1901-1933; Matric inequalities

言語:

英語

目次情報:

Preface / I：

Basic Theory / 1：

Geršgorin's Theorem / 1.1：

Extensions of Geršgorin's Theorem via Graph Theory / 1.2：

Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3：

A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4：

Geršgorin-Type Eigenvalue Inclusion Theorems / 2：

Brauer's Ovals of Cassini / 2.1：

Higher-Order Lemniscates / 2.2：

Comparison of the Brauer Sets and the Brualdi Sets / 2.3：

The Sharpness of Brualdi Lemniscate Sets / 2.4：

An Example / 2.5：

More Eigenvalue Inclusion Results / 3：

The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1：

The Field of Values of a Matrix / 3.2：

Newer Eigenvalue Inclusion Sets / 3.3：

The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4：

Minimal Geršgorin Sets and Their Sharpness / 4：

Minimal Geršgorin Sets / 4.1：

Minimal Geršgorin Sets via Permutations / 4.2：

A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3：

G-Functions / 5：

The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1：

Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2：

Minimal G-Functions / 5.3：

Minimal G-Functions with Small Domains of Dependence / 5.4：

Connections with Brauer Sets and Generalized Brualdi Sets / 5.5：

Geršgorin-Type Theorems for Partitioned Matrices / 6：

Partitioned Matrices and Block Diagonal Dominance / 6.1：

A Different Norm Approach / 6.2：

A Variation on a Theme by Brualdi / 6.3：

G-Functions in the Partitioned Case / 6.4：

Geršgorin's Paper from 1931, and Comments / Appendix A：

Vector Norms and Induced Operator Norms / Appendix B：

The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C：

Matlab 6 Programs / Appendix D：

References

Preface / I：

Basic Theory / 1：

Geršgorin's Theorem / 1.1：

Extensions of Geršgorin's Theorem via Graph Theory / 1.2：

Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3：

A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4：

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