• Home
  • Advanced Search
  • Directory of Libraries
  • About lib.ir
  • Contact Us
  • History

عنوان
Algorithms for the matrix exponential and its Fréchet derivative

پدید آورنده
Al-Mohy, Awad

موضوع
matrix exponential,matrix function,Pad\'e approximation,scaling and squaring method

رده

کتابخانه
Center and Library of Islamic Studies in European Languages

محل استقرار
استان: Qom ـ شهر: Qom

Center and Library of Islamic Studies in European Languages

تماس با کتابخانه : 32910706-025

NATIONAL BIBLIOGRAPHY NUMBER

Number
TLets518467

TITLE AND STATEMENT OF RESPONSIBILITY

Title Proper
Algorithms for the matrix exponential and its Fréchet derivative
General Material Designation
[Thesis]
First Statement of Responsibility
Al-Mohy, Awad
Subsequent Statement of Responsibility
Higham, Nicholas ; Thatcher, Ronald

.PUBLICATION, DISTRIBUTION, ETC

Name of Publisher, Distributor, etc.
University of Manchester
Date of Publication, Distribution, etc.
2011

DISSERTATION (THESIS) NOTE

Dissertation or thesis details and type of degree
Ph.D.
Body granting the degree
University of Manchester
Text preceding or following the note
2011

SUMMARY OR ABSTRACT

Text of Note
New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form \sum_{k=0}^p\varphi_k(A)u_k that arise in exponential integrators, where the \varphi_k are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension

TOPICAL NAME USED AS SUBJECT

matrix exponential
matrix function
Pad\'e approximation
scaling and squaring method

PERSONAL NAME - PRIMARY RESPONSIBILITY

Al-Mohy, Awad

PERSONAL NAME - SECONDARY RESPONSIBILITY

Higham, Nicholas
Thatcher, Ronald

CORPORATE BODY NAME - SECONDARY RESPONSIBILITY

University of Manchester

ELECTRONIC LOCATION AND ACCESS

Electronic name
 مطالعه متن کتاب 

p

[Thesis]
276903

a
Y

Proposal/Bug Report

Warning! Enter The Information Carefully
Send Cancel
This website is managed by Dar Al-Hadith Scientific-Cultural Institute and Computer Research Center of Islamic Sciences (also known as Noor)
Libraries are responsible for the validity of information, and the spiritual rights of information are reserved for them
Best Searcher - The 5th Digital Media Festival