Journal Article10.1137/0714039
Numerical Computation of the Matrix Exponential with Accuracy Estimate
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TL;DR: An algorithm for computing the exponential of an arbitrary $n \times n$ matrix is presented and Diagonal Pade table approximations are used in conjunction with several techniques for reducing the norm of the matrix.
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Abstract: This paper presents and analyzes an algorithm for computing the exponential of an arbitrary $n \times n$ matrix. Diagonal Pade table approximations are used in conjunction with several techniques for reducing the norm of the matrix. An important feature of the algorithm is that an estimate for the minimum number of digits accurate in the norm of the computed exponential matrix is returned to the user. In obtaining this estimate, several interesting results concerning rounding errors and Pade approximations are presented.
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References
Nineteen Dubious Ways to Compute the Exponential of a Matrix
Cleve B. Moler,Charles Van Loan +1 more
TL;DR: In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.
A novel method of evaluating transient response
M.L. Liou
- 01 Jan 1966
TL;DR: In this article, a method of evaluating transient responses of linear time-invariant systems using the state space approach is described, where the Laplace transform of the response function as a ratio of two polynomials in the complex frequency of proper form is formulated.
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Avoiding the Jordan Canonical Form in the Discussion of Linear Systems with Constant Coefficients
TL;DR: In this paper, the Jordan Canonical Form in the discussion of linear systems with constant coefficients has been avoided in the context of linear system with constant coefficients, and the authors propose an alternative approach to avoid it.
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