New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential
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Publication:5251939
DOI10.1137/090763202zbMath1315.65046OpenAlexW1979075532MaRDI QIDQ5251939
Jacinto-Javier Ibáñez, Pedro A. Ruiz, Jorge Sastre, Emilio Defez
Publication date: 21 May 2015
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/10251/63733
Taylor seriesbackward error analysismatrix exponentialscaling and squaringPaterson-Stockmeyer methodcomputational cost analysis
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Uses Software
Cites Work
- Unnamed Item
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- Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods
- Exponential time differencing for stiff systems
- Computing matrix functions
- A practical method for computing the exponential of a matrix and its integral
- Numerical Computation of the Matrix Exponential with Accuracy Estimate
- Exponential Integrators for Large Systems of Differential Equations
- Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
- Accuracy and Stability of Numerical Algorithms
- The Scaling and Squaring Method for the Matrix Exponential Revisited
- Fourth-Order Time-Stepping for Stiff PDEs
- Functions of Matrices
- On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials
- Benchmarking optimization software with performance profiles.
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