Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method

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 ; 235

ISBN:

9783034806121 [3034806124]    

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 second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with qua

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