INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783034806121
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52527
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Separable Type Representations of Matrices and Fast Algorithm
General Material Designation
[Book]
Other Title Information
:Volume 2 Eigenvalue Method
First Statement of Responsibility
/ electronic resource
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Basel
Name of Publisher, Distributor, etc.
: Springer Basel :Imprint: Birkh?user,
Date of Publication, Distribution, etc.
, 2014.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XI, 359 s. , online resource..
SERIES
Series Title
(Operator Theory
Other Title Information
: Advances and Applications
Volume Designation
; 235,0255-0156)
GENERAL NOTES
Text of Note
9783034806114.
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
Summary: 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 quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. 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.
Text of Note
Part 5. The eigenvalue structure of order one quasiseparable matrices -- 21. Quasiseparable of order one matrices -- Characteristic polynomials -- 22. Eigenvalues with geometric multiplicity one -- 23. Kernels of quasiseparable of order one matrices -- 24. Multiple eigenvalues -- Part 6. Divide and conquer method for eigenproblems -- 25. Divide step -- 26. Conquer step and rational matrix functions eigenproblem -- 27. Complete algorithm for Hermitian matrices -- 28. Complete algorithm for unitary Hessenberg matrices -- Part 7. Algorithms for qr iterations and for reduction to Hessenberg form -- 29. The QR iteration method for eigenvalues -- 30. The reduction to Hessenberg form -- 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices -- Part 8. QR iterations for companion matrices -- 32. Companion and unitary matrices -- 33. Explicit methods -- 34. Implicit methods with compression -- 35. The factorization based implicit method -- 36. Implicit algorithms based on the QR representation -- Bibliography -- a.
SERIES
Title
Operator Theory: Advances and Applications ;235,0255-0156
TOPICAL NAME USED AS SUBJECT
Mathematics
Matrix theory
Numerical analysis
Mathematics
Linear and Multilinear Algebras, Matrix Theory
Numerical Analysis
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Eidelman, Yuli.
PERSONAL NAME - SECONDARY RESPONSIBILITY
Gohberg, Israel
Haimovici, Iulian
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783034806114.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783034806114.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
