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The computation of matrix functions in particular, the matrix exponential

Ghufran, Syed Muhammad (2010)
M.Phil. thesis, University of Birmingham.

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Abstract

Matrix functions in general are an interesting area in matrix analysis and are used in many areas of linear algebra and arise in numerous applications in science and engineering. We consider how to define matrix functions and how to compute matrix functions. To be concrete, we pay particular attention to the matrix exponential. The matrix exponential is one of the most important functions of a matrix. In this thesis, we discuss some of the more common matrix functions and their general properties, and we specifcally explore the matrix exponential. In principle, there are many different methods to calculate the exponential of a matrix. In practice, some of the methods are preferable to others, but none of which is entirely satisfactory from either a theoretical or a computational point of view. Computations of the matrix exponential using Taylor Series, Pade Approximation, Scaling and Squaring, Eigenvectors and Schur Decomposition methods are provided. In this project we checked rate of convergence and accuracy of the matrix exponential.

Type of Work:M.Phil. thesis.
Supervisor(s):Mathias, Roy
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:922
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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