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