Matrix computations and semiseparable matrices. V.2. Eigenvalue and singular value methods / Raf Vandebril, Marc Van Barel, Nicola Mastronardi.

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Bibliographic Details
Main Author: Vandebril, Raf, 1978-
Other Authors: Barel, Marc van, 1960-, Mastronardi, Nicola, 1962-
Format: eBook
Language:English
Published: Baltimore : Johns Hopkins University Press, 2008-
Subjects:
Online Access:Click for online access

MARC

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100 1 |a Vandebril, Raf,  |d 1978- 
245 1 0 |a Matrix computations and semiseparable matrices.  |n V.2.  |p Eigenvalue and singular value methods /  |c Raf Vandebril, Marc Van Barel, Nicola Mastronardi. 
260 |a Baltimore :  |b Johns Hopkins University Press,  |c 2008- 
300 |a 1 online resource :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references and indexes. 
505 0 |a ""Contents""; ""Preface""; ""Notation""; ""1 Introduction to semiseparable matrices""; ""1.1 Definition of semiseparable matrices""; ""1.2 Some properties""; ""1.2.1 Relations under inversion""; ""1.2.2 Generator representable semiseparable matrices""; ""1.3 The representations""; ""1.3.1 The generator representation""; ""1.3.2 The Givens-vector representation""; ""1.4 Conclusions""; ""I: The reduction of matrices""; ""2 Algorithms for reducing matrices""; ""2.1 Introduction""; ""2.2 Orthogonal similarity transformations of symmetric matrices"" 
505 8 |a ""2.3 Orthogonal similarity transformation of (unsymmetric) matrices""""2.4 Orthogonal transformations of matrices""; ""2.5 Transformations from sparse to structured rank form""; ""2.6 From structured rank to sparse form""; ""2.7 Conclusions""; ""3 Convergence properties of the reduction algorithms""; ""3.1 The Arnoldi(Lanczos)-Ritz values""; ""3.2 Subspace iteration inside the reduction algorithms""; ""3.3 Interaction of the convergence behaviors""; ""3.4 Conclusions""; ""4 Implementation of the algorithms and numerical experiments""; ""4.1 Working with Givens transformations"" 
505 8 |a ""4.2 Implementation details""""4.3 Numerical experiments""; ""4.4 Conclusions""; ""II: QR-algorithms (eigenvalue problems)""; ""5 Introduction: traditional sparse QR-algorithms""; ""5.1 On the QR-algorithm""; ""5.2 A QR-algorithm for sparse matrices""; ""5.3 An implicit QR-method for sparse matrices""; ""5.4 On computing the singular values""; ""5.5 Conclusions""; ""6 Theoretical results for structured rank QR-algorithms""; ""6.1 Preserving the structure under a QR-step""; ""6.2 An implicit Q-theorem""; ""6.3 On Hessenberg-like plus diagonal matrices""; ""6.4 Conclusions"" 
505 8 |a ""7 Implicit QR-methods for semiseparable matrices""""7.1 An implicit QR-algorithm for symmetric semiseparable matrices""; ""7.2 A QR-algorithm for semiseparable plus diagonal""; ""7.3 An implicit QR-algorithm for Hessenberg-like matrices""; ""7.4 An implicit QR-algorithm for computing the singular values""; ""7.5 Conclusions""; ""8 Implementation and numerical experiments""; ""8.1 Working with Givens transformations""; ""8.2 Implementation of the QR-algorithm for semiseparable matrices""; ""8.3 Computing the eigenvectors""; ""8.4 Numerical experiments""; ""8.5 Conclusions"" 
505 8 |a ""9 More on QR-related algorithms""""9.1 Complex arithmetic and Givens transformations""; ""9.2 Variations of the QR-algorithm""; ""9.3 The QR-method for quasiseparable matrices""; ""9.4 The multishift QR-algorithm""; ""9.5 A QH-algorithm""; ""9.6 Computing zeros of polynomials""; ""9.7 References to related subjects""; ""9.8 Conclusions""; ""III: Some generalizations and miscellaneous topics""; ""10 Divide-and-conquer algorithms for the eigendecomposition""; ""10.1 Arrowhead and diagonal plus rank 1 matrices""; ""10.2 Divide-and-conquer algorithms for tridiagonal matrices"" 
650 0 |a Semiseparable matrices. 
650 0 |a Matrices  |x Data processing. 
650 0 |a Numerical analysis. 
650 7 |a MATHEMATICS.  |2 bisac 
650 7 |a Matrices.  |2 bisac 
650 7 |a Matrices  |x Data processing  |2 fast 
650 7 |a Numerical analysis  |2 fast 
650 7 |a Semiseparable matrices  |2 fast 
700 1 |a Barel, Marc van,  |d 1960- 
700 1 |a Mastronardi, Nicola,  |d 1962- 
758 |i has work:  |a Volume 2 Eigenvalue and singluar value methods Matrix computations and semiseparable matrices (Text)  |1 https://id.oclc.org/worldcat/entity/E39PCGfQwJPjHDQMKtY7Wxh3FC  |4 https://id.oclc.org/worldcat/ontology/hasWork 
776 0 8 |i Print version:  |a Vandebril, Raf.  |t Matrix Computations and Semiseparable Matrices Vol. 2 : Eigenvalue and Singular Value Methods.  |d Baltimore : Johns Hopkins University Press, ©1900  |z 9780801890529 
856 4 0 |u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=3318462  |y Click for online access 
903 |a EBC-AC 
994 |a 92  |b HCD