Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms

種類:

電子ブック

責任表示:

by Yuli Eidelman, Israel Gohberg, Iulian Haimovici

出版情報:

Basel : Springer Basel : Imprint: Birkhäuser, 2014

著者名:

• Eidelman, Yuli
• Gohberg, Israel
• Haimovici, Iulian
• SpringerLink (Online service)

シリーズ名:

Operator Theory: Advances and Applications ; 234

ISBN:

9783034806060 [303480606X]    

注記:

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

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