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Matrix Computations and Semiseparable Matrices

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, 584 pages

7 halftones, 75 line drawings

December 2007



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Matrix Computations and Semiseparable Matrices

Linear Systems

Volume 1

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices.

The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Raf Vandebril is a researcher in the Department of Computer Science at Katholieke Universiteit Leuven, Belgium. Marc Van Barel is a professor of computer science at Katholieke Universiteit Leuven, Belgium. Nicola Mastronardi is a researcher at the M. Picone Institute for Applied Mathematics, Bari, Italy.

"In particular, the relation with algorithms of historical interest will make the book interesting for its readers."

"An indispensable tool for scholars and research workers in mathematics and the mathematical sciences."

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