The Exponentially Convergent Trapezoidal Rule
University of Oxford · Stellenbosch University
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Abstract
It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed, and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.
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551
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- 28.90
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- 100%
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Authors
2Topics & keywords
Topics
Keywords
- Eigenvalues and eigenvectors
- Mathematics
- Laplace transform
- Inverse Laplace transform
- Computation
- Trapezoidal rule
- Applied mathematics
- Real line
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