Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation

  • Erich L. Kaltofen*
  • , Wen Shin Lee
  • , Zhengfeng Yang
  • *Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations

Abstract

We investigate our early termination criterion for sparse polynomial interpolation when substantial noise is present in the values of the polynomial. Our criterion in the exact case uses Monte Carlo randomization which introduces a second source of error. We harness the Gohberg-Semencul formula for the inverse of a Hankel matrix to compute estimates for the structured condition numbers of all arising Hankel matrices in quadratic arithmetic time overall, and explain how false ill-conditionedness can arise from our randomizations. Finally, we demonstrate by experiments that our condition number estimates lead to a viable termination criterion for polynomials with about 20 non-zero terms and of degree about 100, even in the presence of noise of relative magnitude 10 -5.

Original languageEnglish
Title of host publicationSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Pages130-136
Number of pages7
DOIs
StatePublished - 2011
EventSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - San Jose, CA, United States
Duration: 7 Jun 20119 Jun 2011

Publication series

NameSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation

Conference

ConferenceSNC'11 - Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Country/TerritoryUnited States
CitySan Jose, CA
Period7/06/119/06/11

Keywords

  • Early termination
  • Gohberg-Semencul formula
  • Hankel system
  • Sparse polynomial interpolation
  • Vandermonde system

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