Mitsuhiro T. Nakao, Yoshitaka Watanabe and Nobito Yamamoto:
Verified Numerical Computations for an Inverse Elliptic Eigenvalue Problem with Finite Data,
Japan Journal of Industrial and Applied Mathematics, Vol.18, No.2 (2001) pp.567-585.

We consider a numerical enclosure method for solutions of an inverse Dirichlet eigenvalue problem. When the finite number of prescribed eigenvalues are given, we recontruct 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 a numerical example which confirms us the enclosure algorithm works on a real problem.

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