【令和２（２０２０）年度の成果】
年度代表論文
[1] T. Hoshi, T. Ogita, K. Ozaki, T. Terao: An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations, Journal of Computational and Applied Mathematics, Volume 376, 2020, 112830. DOI: 10.1016/j.cam.2020.112830
[2] M. Lange, S. Oishi: A note on Dekker’s FastTwoSum algorithm, Numerische Mathematik, Volume 145, 383?403, 2020. DOI: 10.1007/s00211-020-01114-2
[3] K. Tanaka: Numerical verification method for positive solutions of elliptic problems, Journal of Computational and Applied Mathematics, Volume 370, 2020, 112647. DOI: 10.1016/j.cam.2019.112647
[4] Y. Watanabe, T. Kinoshita, M.T. Nakao: Some improvements of invertibility verifications for second-order linear elliptic operators, Applied Numerical Mathematics, Volume 154, 36-46, 2020. DOI: 10.1016/j.apnum.2020.03.016
[5] K. Sekine, M.T. Nakao, S. Oishi: A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator, Numerische Mathematik, Volume 146, 907?926, 2020. DOI: 10.1007/s00211-020-01155-7
実績報告書（JSTページにリンク）
【令和元（２０１９）年度の成果】
年度代表論文
[1] T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues, Japan J. Indust. Appl. Math., 36:2 (2019), pp. 435-459.
[2] T.Kinoshita, Y.Watanabe, M.T. Nakao: An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces, J.Differ.Equ., 266:9 (2019),pp. 5431-5447.
[3] K.Endo: New approach to evaluate the asymptotic distribution of particle systems expressed by probabilistic cellular automata, Japan J. Indust. Appl. Math.,37 (2020), pp. 461-484.
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【平成３０（２０１８）年度の成果】
年度代表論文
[1]T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition, Japan Journal of Industrial and Applied Mathematics, Vol. 35, Issue 3, pp. 1007-1035, 2018.
[2]X. Liu, F. Kikuchi: Explicit estimation of error constants appearing in non-conforming linear triangular finite element method, Applications of Mathematics, Vol. 63, Issue 4, pp. 381–397, 2018.
[3]Y. Tokieda, D. Takahashi: Max-plus equation with two conserved quantities and one monotonically decreasing quantity, JSIAM Letters, Vol.10, pp. 45-48, 2018.
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【平成２９（２０１７）年度の成果】
年度代表論文
[1] Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, and Shin’ichi Oishi, A method of verified computations for solutions to semilinear parabolic equations using semigroup theory, SIAM J. Numer. Anal.,Vol. 55, No.2, pp.980-1001, 2017.
[2] A. Takayasu, K. Matsue, T. Sasaki, K. Tanaka, M. Mizuguchi, and S. Oishi: Numerical validation of blow-up solutions of ordinary differential equations, J. Comput. Appl. Math., Vol. 314, pp.10-29, Apr. 2017.
[3] Ryo Kobayashi, Takuma Kimura, Shin’ichi Oishi, A method for verifying the accuracy of numerical solutions of symmetric saddle point linear systems, Numerical Algorithms, Vol. 76, Issue 1, pp.33–51, September 2017.
実績報告書（JSTページにリンク）
【平成２８（２０１６）年度の成果】
年度代表論文
[1] M. Mizuguchi, A. Takayasu, T. Kubo,S. Oishi: Numerical verification for existence of a global-in-time solution to semilinear parabolic equations, J. Comput. Appl. Math., Vol. 315, pp. 1-16, 2017.
[2] Y. Watanabe, K. Nagatou, M. Plum, M. T. Nakao: Norm Bound Computation for Inverses of Linear Operators in Hilbert Spaces, Journal of Differential Equations, Vol. 260, Issue 7, pp. 6363-6374, 2016.
[3] K. Ozaki, T. Ogita, S. Oishi: Error-free transformation of matrix multiplication with a posteriori validation, Numerical Linear Algebra with Applications, Vol. 23, No. 5, pp. 931-946, 2016.
実績報告書（JSTページにリンク）
【平成２７（２０１５）年度の成果】
年度代表論文
[1] Y. Watanabe, M. T. Nakao: A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration, Applied Mathematics and Computation, Vol. 276, Issue C (2016), pp.239-251.
[2] K. Kobayashi,T. Tsuchiya: A priori error estimates for Lagrange interpolation on 4 triangles, Applications of Mathematics, Vol.60, Issue 5 (2015), pp.485-499.
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【平成２６（２０１４）年度の成果】
実績報告書（JSTページにリンク）