Numerical Methods and Algorithms

The Schur Complement and Its Applications

Editors: Zhang, Fuzhen (Ed.)

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About this book

The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. This book 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. The eight chapters of the book cover themes and variations 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 applications in statistics, probability, and numerical analysis. The chapters need not be read in order, and the reader should feel free to browse freely through topics of interest.

Although the book is primarily intended to serve as a research reference, it will also be useful for graduate and advanced undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors’ exposition makes most of the material accessible to readers with a sound foundation in linear algebra.

The book, edited by Fuzhen Zhang, was written by several distinguished mathematicians: T. Ando (Hokkaido University, Japan), C. Brezinski (Université des Sciences et Technologies de Lille, France), R. Horn (University of Utah, Salt Lake City, U.S.A.), C. Johnson (College of William and Mary, Williamsburg, U.S.A.), J.-Z. Liu (Xiangtang University, China), S. Puntanen (University of Tampere, Finland), R. Smith (University of Tennessee, Chattanooga, USA), and G.P.H. Steyn (McGill University, Canada). Fuzhen Zhang is a professor of Nova Southeastern University, Fort Lauderdale, U.S.A., and a guest professor of Shenyang Normal University, Shenyang, China.

Audience

This book is intended for researchers in linear algebra, matrix analysis, numerical analysis, and statistics.

Reviews

From the reviews of the first edition:

"The book consists of eight chapters, each written by experts in their field, devoted to certain aspects and applications of the Schur complement. They can be read independently of each other. … The book can serve as a research reference, as it contains many new results and results not yet appeared in books. The articles contain thorough expositions, so they can be understood by anyone having a good knowledge of linear algebra." (Ludwig Elsner, Zentralblatt MATH, Vol. 1075, 2006)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • Historical Introduction: Issai Schur and the Early Development of the Schur Complement

    Pages 1-16

    Puntanen, Simo (et al.)

  • Basic Properties of the Schur Complement

    Pages 17-46

    Horn, Roger A. (et al.)

  • Eigenvalue and Singular Value Inequalities of Schur Complements

    Pages 47-82

    Liu, Jianzhou

  • Block Matrix Techniques

    Pages 83-110

    Zhang, Fuzhen

  • Closure Properties

    Pages 111-136

    Johnson, Charles R. (et al.)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-0-387-24273-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-0-387-24271-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $139.99
price for USA in USD
  • ISBN 978-1-4419-3712-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
The Schur Complement and Its Applications
Editors
  • Fuzhen Zhang
Series Title
Numerical Methods and Algorithms
Series Volume
4
Copyright
2005
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-24273-6
DOI
10.1007/b105056
Hardcover ISBN
978-0-387-24271-2
Softcover ISBN
978-1-4419-3712-4
Series ISSN
1571-5698
Edition Number
1
Number of Pages
XVI, 295
Topics