The Schur Complement and Its Applications

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Beschreibung

What's in a name? To paraphrase Shakespeare's Juliet, that which - ilie Haynsworth called the Schur complement, by any other name would be just as beautiful. Nevertheless, her 1968 naming decision in honor of Issai Schur (1875-1941) has gained lasting acceptance by the mathematical com munity. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. Our goal is to expose the Schur complement as a rich and basic tool in mathematical research and applications and to discuss many significant re sults that illustrate its power and fertility. Although our book was originally conceived as a research reference, it will also be useful for graduate and up per division undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors have developed an exposition that makes the material accessible to readers with a sound foundation in linear algebra. The eight chapters of the book (Chapters 0-7) cover themes and varia tions on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and appli cations in statistics, probability, and numerical analysis. The chapters need not be read in the order presented, and the reader should feel at leisure to browse freely through topics of interest.

Zusammenfassung

Describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility

Includes supplementary material: [...]

Inhaltsverzeichnis

Historical Introduction: Issai Schur and the Early Development of the Schur Complement.- Basic Properties of the Schur Complement.- Eigenvalue and Singular Value Inequalities of Schur Complements.- Block Matrix Techniques.- Closure Properties.- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach.- Schur complements in statistics and probability.- Schur Complements and Applications in Numerical Analysis.

Details

Erscheinungsjahr:	2005
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xvi 295 S.
ISBN-13:	9780387242712
ISBN-10:	0387242716
Sprache:	Englisch
Einband:	Gebunden
Autor:	Zhang, F.
Redaktion:	Zhang, Fuzhen
Herausgeber:	Fuzhen Zhang
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 22 mm
Von/Mit:	Fuzhen Zhang
Erscheinungsdatum:	04.03.2005
Gewicht:	0,635 kg

Artikel-ID: 102327640

Zusammenfassung

Describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility

Includes supplementary material: [...]

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2005
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xvi 295 S.
ISBN-13:	9780387242712
ISBN-10:	0387242716
Sprache:	Englisch
Einband:	Gebunden
Autor:	Zhang, F.
Redaktion:	Zhang, Fuzhen
Herausgeber:	Fuzhen Zhang
Hersteller:	Springer US Springer New York Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 22 mm
Von/Mit:	Fuzhen Zhang
Erscheinungsdatum:	04.03.2005
Gewicht:	0,635 kg