### 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 language | English |
---|---|

Pages (from-to) | 587-602 |

Number of pages | 16 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 18 |

Issue number | 2 |

Publication status | Published - 2001 Jun |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Japan Journal of Industrial and Applied Mathematics*,

*18*(2), 587-602.

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

Research output: Contribution to journal › Article

*Japan Journal of Industrial and Applied Mathematics*, vol. 18, no. 2, pp. 587-602.

}

TY - JOUR

T1 - Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data

AU - Nakao, Mitsuhiro T.

AU - Watanabe, Yoshitaka

AU - Yamamoto, Nobito

PY - 2001/6

Y1 - 2001/6

N2 - 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.

AB - 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.

KW - Computer assisted proof

KW - Inverse elliptic eigenvalue problem

KW - Numerical verification method

UR - http://www.scopus.com/inward/record.url?scp=0347670249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347670249&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347670249

VL - 18

SP - 587

EP - 602

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2

ER -