Bøger i Numerical Methods and Algorithms serien

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.

This book introduces the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. This new edition offers improved content and more explanation for the non-expert.

This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms.

Aims to create a bridge between control theory and its numerical analysis aspects. This book combines an exposition of linear control theory and the corresponding modern relevant computational techniques such as orthogonal polynomials, numerical linear algebra, and more. It is useful for advanced students at a doctoral or post-doctoral level.

The present book - through the topics and the problems approach - aims at filling a gap, a real need in our literature concerning CFD (Computational Fluid Dynamics).

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.