Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data

Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto

Research output: Contribution to journalArticle

Abstract

We consider a numerical enclosure method for solutions of an inverse Dirichlet eigenvalue problem. When the finite number of prescribed eigenvalues are given, we reconstruct a potential function, with guaranteed error bounds, for which the corresponding elliptic operator exactly has those eigenvalues including the ordering property. All computations are executed with numerical verifications based upon the finite and infinite fixed point theorems using interval arithmetic. Therefore, the results obtained are mathematically correct. We present numerical examples which confirm us the enclosure algorithm works on real problems.

Original languageEnglish
Pages (from-to)587-602
Number of pages16
JournalJapan Journal of Industrial and Applied Mathematics
Volume18
Issue number2
Publication statusPublished - 2001 Jun
Externally publishedYes

Fingerprint

Enclosure
Enclosures
Elliptic Problems
Numerical Computation
Eigenvalue Problem
Eigenvalue
Dirichlet Eigenvalues
Numerical Verification
Interval Arithmetic
Potential Function
Elliptic Operator
Dirichlet Problem
Error Bounds
Fixed point theorem
Numerical Examples

Keywords

  • Computer assisted proof
  • Inverse elliptic eigenvalue problem
  • Numerical verification method

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data. / Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 18, No. 2, 06.2001, p. 587-602.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Watanabe, Yoshitaka ; Yamamoto, Nobito. / Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data. In: Japan Journal of Industrial and Applied Mathematics. 2001 ; Vol. 18, No. 2. pp. 587-602.
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