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A Numerical Investigation of Different Methods for Computing the Matrix Exponential

(2021) In Bachelor’s Theses in Mathematical Sciences NUMK11 20202
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
Matrix functions and their applications play an important role in different fields of science and engineering. The matrix exponential is one of the most important and extensively used function of matrices. The computation of the exponential of a matrix is an interesting topic that has been extensively studied over the years. There are several ways computing the matrix exponential but there is a puzzle about which method is best.

The foundation of this thesis project is a classic paper from 1978 which highlights most of these methods. An updated version was published in 2003. There have been further improvements on these methods since then but the core algorithms remain the same, hence the paper is still relevant. This thesis project is... (More)
Matrix functions and their applications play an important role in different fields of science and engineering. The matrix exponential is one of the most important and extensively used function of matrices. The computation of the exponential of a matrix is an interesting topic that has been extensively studied over the years. There are several ways computing the matrix exponential but there is a puzzle about which method is best.

The foundation of this thesis project is a classic paper from 1978 which highlights most of these methods. An updated version was published in 2003. There have been further improvements on these methods since then but the core algorithms remain the same, hence the paper is still relevant. This thesis project is devoted to implementing the various methods of computing the matrix exponential, comparing these methods, and finally determining the best method in terms of generality, reliability, stability, accuracy, and efficiency. (Less)
Popular Abstract (Swedish)
Matrisfunktioner och deras applikationer spelar en viktig roll inom olika vetenskaps- och teknikområden. Matrisexponentialen är en av de viktigaste och mest använda funktionerna av matriser. Beräkningen av exponentialen av en matris är ett intressant ämne som har studerats mycket genom åren. Det finns flera sätt att beräkna matrisexponentialen men det är en utmaning att hitta vilken metod som är bäst.

Grunden för detta examensarbete är en klassisk artikel från 1978 som berör de flesta av dessa metoder. En uppdaterad version publicerades 2003. Det har gjorts ytterligare förbättringar av dessa metoder sedan dess, men grunden i de olika algoritmerna är densamma, därför är artikeln fortfarande relevant. Detta examensarbete går ut på att... (More)
Matrisfunktioner och deras applikationer spelar en viktig roll inom olika vetenskaps- och teknikområden. Matrisexponentialen är en av de viktigaste och mest använda funktionerna av matriser. Beräkningen av exponentialen av en matris är ett intressant ämne som har studerats mycket genom åren. Det finns flera sätt att beräkna matrisexponentialen men det är en utmaning att hitta vilken metod som är bäst.

Grunden för detta examensarbete är en klassisk artikel från 1978 som berör de flesta av dessa metoder. En uppdaterad version publicerades 2003. Det har gjorts ytterligare förbättringar av dessa metoder sedan dess, men grunden i de olika algoritmerna är densamma, därför är artikeln fortfarande relevant. Detta examensarbete går ut på att implementera de olika metoderna för beräkning av matrisexponentialen, jämföra dessa metoder och slutligen avgöra vilken av metoderna som är bäst. (Less)
author
supervisor
organization
course
NUMK11 20202
year
type
M2 - Bachelor Degree
subject
keywords
matrix exponential, algorithms, efficiency, accuracy
publication/series
Bachelor’s Theses in Mathematical Sciences
report number
LUNFNA-4035-2021
ISSN
1654-6229
other publication id
2021:K2
language
English
id
9041181
2021-03-16 14:13:44
date last changed
2021-03-16 14:13:44
```@misc{9041181,
abstract     = {{Matrix functions and their applications play an important role in different fields of science and engineering. The matrix exponential is one of the most important and extensively used function of matrices. The computation of the exponential of a matrix is an interesting topic that has been extensively studied over the years. There are several ways computing the matrix exponential but there is a puzzle about which method is best.

The foundation of this thesis project is a classic paper from 1978 which highlights most of these methods. An updated version was published in 2003. There have been further improvements on these methods since then but the core algorithms remain the same, hence the paper is still relevant. This thesis project is devoted to implementing the various methods of computing the matrix exponential, comparing these methods, and finally determining the best method in terms of generality, reliability, stability, accuracy, and efficiency.}},
author       = {{Cherotich, Yvonne}},
issn         = {{1654-6229}},
language     = {{eng}},
note         = {{Student Paper}},
series       = {{Bachelor’s Theses in Mathematical Sciences}},
title        = {{A Numerical Investigation of Different Methods for Computing the Matrix Exponential}},
year         = {{2021}},
}

```