The Schur Complement and Its Applications

Buch | Hardcover

295 Seiten

2005
Springer-Verlag New York Inc.
978-0-387-24271-2 (ISBN)

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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. This title covers such topics as historical development, basic properties, eigenvalue and singular value inequalities, closure properties, and applications in statistics.

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.

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.

Reihe/Serie	Numerical Methods and Algorithms ; 4
Zusatzinfo	XVI, 295 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-387-24271-6 / 0387242716
ISBN-13	978-0-387-24271-2 / 9780387242712
Zustand	Neuware