article · Japan Journal of Industrial and Applied Mathematics · 2023

Numerical analytic continuation

Cited by 28Open access

Abstract

Abstract Let f be an analytic function on a simply-connected compact continuum E of the complex z -plane. This might be an interval of the real line, where f might be real analytic. How can we calculate good estimates of the analytic continuation of f to other points $$z\in {\mathbb C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>z</mml:mi><mml:mo>∈</mml:mo><mml:mi>C</mml:mi></mml:mrow></mml:math> ? How can we estimate the locations of real or complex singularities of f ? We review both the theory and the practice of some existing methods for these problems and propose that excellent results can be obtained from the computation of rational approximations of f by the AAA algorithm. In the case of analytic functions of two or more variables, the rational approximations are applied along line segments or other analytic arcs.

Cite this paper

APA 7

Trefethen, L. N. (2023). Numerical analytic continuation. Japan Journal of Industrial and Applied Mathematics, 40(3), 1587–1636. https://doi.org/10.1007/s13160-023-00599-2

MLA 9

Trefethen, Lloyd N. “Numerical analytic continuation.” Japan Journal of Industrial and Applied Mathematics, vol. 40, no. 3, 2023, pp. 1587–636, https://doi.org/10.1007/s13160-023-00599-2.

Chicago

Trefethen, Lloyd N. 2023. “Numerical analytic continuation.” Japan Journal of Industrial and Applied Mathematics 40 (3): 1587–636. https://doi.org/10.1007/s13160-023-00599-2.

Harvard

Trefethen, L.N. (2023) ‘Numerical analytic continuation’, Japan Journal of Industrial and Applied Mathematics, 40(3), pp. 1587–1636. Available at: https://doi.org/10.1007/s13160-023-00599-2.

BibTeX

@article{trefethen2023numerical,
  title = {{Numerical analytic continuation}},
  author = {Trefethen, Lloyd N.},
  journal = {Japan Journal of Industrial and Applied Mathematics},
  volume = {40},
  number = {3},
  pages = {1587--1636},
  year = {2023},
  doi = {10.1007/s13160-023-00599-2}
}

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