TY - JOUR
T1 - Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators
AU - Toyonaga, K.
AU - Nakao, M. T.
AU - Watanabe, Y.
PY - 2002/10/1
Y1 - 2002/10/1
N2 - In this paper, we propose a numerical method to verify bounds for multiple eigenvalues for elliptic eigenvalue problems. We calculate error bounds for approximations of multiple eigenvalues and base functions of the corresponding invariant subspaces. For matrix eigenvalue problems, Rump (Linear Algebra Appl. 324 (2001) 209) recently proposed a validated numerical method to compute multiple eigenvalues. In this paper, we extend his formulation to elliptic eigenvalue problems, combining it with a method developed by one of the authors (Jpn. J. Indust. Appl. Math. 16 (1998) 307).
AB - In this paper, we propose a numerical method to verify bounds for multiple eigenvalues for elliptic eigenvalue problems. We calculate error bounds for approximations of multiple eigenvalues and base functions of the corresponding invariant subspaces. For matrix eigenvalue problems, Rump (Linear Algebra Appl. 324 (2001) 209) recently proposed a validated numerical method to compute multiple eigenvalues. In this paper, we extend his formulation to elliptic eigenvalue problems, combining it with a method developed by one of the authors (Jpn. J. Indust. Appl. Math. 16 (1998) 307).
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U2 - 10.1016/S0377-0427(02)00431-4
DO - 10.1016/S0377-0427(02)00431-4
M3 - Article
AN - SCOPUS:0036772161
SN - 0377-0427
VL - 147
SP - 175
EP - 190
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -