Separable type representations of matrices and fast algorithms. Volume 1, [electronic resource] Basics. Completion Problems. Multiplication and Inversion Algorithms / Yuli Eidelman, Israel Gohberg, Iulian Haimovici.

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Separable type representations of matrices and fast algorithms. Volume 1, [electronic resource] Basics. Completion Problems. Multiplication and Inversion Algorithms / Yuli Eidelman, Israel Gohberg, Iulian Haimovici.

9783034806060 electronic book
303480606X electronic book
9783034806053

Basel : Birkhäuser, 2014.

English

1 online resource (xv, 399 pages).

10.1007/978-3-0348-0606-0 doi

QA188

512.9/434

This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.

Includes bibliographical references and index.

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Description based on online resource; title from PDF title page (SpringerLink, viewed October 14, 2013).

Operator theory, advances and applications ; v.234.

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