Pseudospectral Fourier reconstruction with IPRM

Authors Karlheinz Gröchenig, Tomasz Hrycak

Thumbnail PDF


  • Filesize: 108 kB
  • 3 pages

Document Identifiers

Author Details

Karlheinz Gröchenig
Tomasz Hrycak

Cite AsGet BibTex

Karlheinz Gröchenig and Tomasz Hrycak. Pseudospectral Fourier reconstruction with IPRM. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


We generalize the Inverse Polynomial Reconstruction Method (IPRM) for mitigation of the Gibbs phenomenon by reconstructing a function as an algebraic polynomial of degree $n-1$ from the function's $m$ lowest Fourier coefficients ($m ge n$). We compute approximate Legendre coefficients of the function by solving a linear least squares problem, and we show that the condition number of the problem does not exceed $sqrtfrac{m}{{m-alpha_0 n^2}}$, where $alpha_0 = frac{4sqrt{2}}{pi^2} = 0.573 ldots$. Consequently, whenever mbox{$m ge n^2$,} the convergence rate of the modified IPRM for an analytic function is root exponential on the whole interval of definition. Stability and accuracy of the proposed algorithm are validated with numerical experiments.
  • IPRM
  • Fourier series
  • inverse methods
  • pseudospectral methods


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail