Journal Article10.1137/0714039
Numerical Computation of the Matrix Exponential with Accuracy Estimate
239
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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A Matricial Exponentially Fitted Scheme for the Numerical Solution of Stiff Initial-Value Problems
TL;DR: An exponentially fitted scheme for the numerical integration of stiff systems of initial-value problems using Ward's scaling and squaring algorithm and the results of some numerical experiments allow an appraisal of the proposed approach with other methods.
A trust region algorithm for finite-strain plasticity with strongly coupled hardening
P. Areias,N. Silvestre,X. Zhuang +2 more
- 16 Oct 2024
TL;DR: A trust region algorithm and partitioned approach are introduced for finite-strain plasticity with strongly coupled hardening, improving robustness and efficiency by efficiently solving nonlinear equations and reducing drifting, particularly for large strains and anisotropic yield functions.
The Padé–approximation for matrix exponentials applied to an integration algorithm preserving plastic incompressibility
TL;DR: The exponential update formalism is applied to an integration algorithm for rate–independent single crystal plasticity to fulfill the compelling constraint of plastic incompressibility.
Bibliography of the Book Matrix Computations
Gene H. Golub,Charles Van Loan,Christopher C. Paige,Clement Pellerin,Nelson H. F. Beebe +4 more
- 01 Jan 1999
TL;DR: This bibliography is from the book Matrix Computations, Second Edition, by Gene H. Golub and Charles F. Van Loan, The Johns Hopkins University Press, Baltimore, Maryland 21218, 1989.
Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
João R. Cardoso,F. Silva Leite +1 more
TL;DR: Two widely used methods for computing matrix exponentials and matrix logarithms are improved by exploiting the special structure of skew-symmetric and orthogonal matrices by combining Pade approximation and scaling and squaring.
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.
161
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.
153