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
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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 -