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Construction of new generalizations of Wynn’s epsilon and rho algorithm by solving finite difference equations in the transformation order

  • Xiang-Ke Chang
  • Yi HeEmail author
  • Xing-Biao Hu
  • Jian-Qing Sun
  • Ernst Joachim Weniger
Original Paper
  • 13 Downloads

Abstract

We construct new sequence transformations based on Wynn’s epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn’s epsilon and rho algorithm and of Osada’s generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series.

Keywords

Convergence acceleration algorithm Sequence transformation Epsilon algorithm Rho algorithm 

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Notes

Funding information

Y. He was supported by the National Natural Science Foundation of China (Grant No. 11571358), the China Postdoctoral Science Foundation funded project (Grant Nos. 2012M510186 and 2013T60761), and the Youth Innovation Promotion Association CAS. X.K. Chang was supported by the National Natural Science Foundation of China (Grant Nos. 11701550, 11731014) and the Youth Innovation Promotion Association CAS. X.B. Hu was supported by the National Natural Science Foundation of China (Grant Nos. 11871336, 11571358). J.Q. Sun was supported by the Fundamental Research Funds for the Central Universities (201964008), and the National Natural Science Foundation of China (Grant Nos. 11401546, 11871444).

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Authors and Affiliations

  1. 1.LSEC, ICMSEC, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.Wuhan Institute of Physics and MathematicsChinese Academy of SciencesWuhanPeople’s Republic of China
  4. 4.School of Mathematical SciencesOcean University of ChinaQingdaoPeople’s Republic of China
  5. 5.Institut für Physikalische und Theoretische ChemieUniversität RegensburgRegensburgGermany

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