TY - JOUR
T1 - Some considerations of the invertibility verifications for linear elliptic operators
AU - Nakao, Mitsuhiro T.
AU - Watanabe, Yoshitaka
AU - Kinoshita, Takehiko
AU - Kimura, Takuma
AU - Yamamoto, Nobito
PY - 2015
Y1 - 2015
N2 - This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.
AB - This paper presents three computer-assisted procedures for verifying the invertibility of second-order linear elliptic operators and for computing a bound on the norm of its inverse. One of these procedures is an improvement of a theorem by Nakao et al. (Computing 75:1–14, 2005) that uses projection and constructive a priori error estimates and was proposed by two of the authors of this paper. Results verifying these procedures are presented for several numerical examples.
KW - Computer-assisted proof
KW - Differential operators
KW - Numerical verification
KW - Solvability of linear problem
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U2 - 10.1007/s13160-014-0160-6
DO - 10.1007/s13160-014-0160-6
M3 - Article
AN - SCOPUS:84925497299
VL - 32
SP - 19
EP - 31
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 1
ER -