Yamamoto, Nobito

Professor, Department of Computer Science, The University of Electro-Communications

E-mail:

Membership:The Japan Society for Industrial and Applied Mathematics, The Mathematical Society of Japan
Research fields:Numerical analysis, Self-validating numerics, Numerical verification methods for PDE's
Keywords:Verified Numerical Computation, Numerical Methods with Guaranteed accuracy, Computer Assisted Proof, Interval Arithmetic, Finite Element Methods

Curriculum Vitae:

Family name:Yamamoto
Forenames:Nobito

Office address: 1-5-1 Chofu-ga-oka, Chofu, Tokyo, Japan 182-8585

Education:
1979-1984Faculty of Science, Kyoto University (Bachelor of Science)
1984-1986Postgraduate school of Kyoto University (Master of Engineering)
1993Received the degree of Doctor of Science from Kyushu University

Occupation:
1987-1994Research Associate, Department of Mathematics, Faculty of Science, Kyushu University.
1994-1999Lecturer, Graduate School of Mathematics, Kyushu University.
1999-2006   Associate Professor, Department of Computer Science, The University of Electro-Communications
2006-present   Professor, Department of Computer Science, The University of Electro-Communications

Papers:
  1. Yamamoto, N. : Uniqueness and existence of the solution of a diffusion equation with moving boundaries, Mem. Fac. Sci. Kyushu Univ. Ser.A, Vol.45 (1991) 19-40.
  2. Nakao, M.T. and Yamamoto, N. : Numerical verifications of solutions for elliptic equations with strong nonlinearity, Numer. Funct. Anal. and Optimiz., Vol.12 (1991) 535-543.
  3. Kumamoto, S., Yamamoto, N. and Nohmi, M. : On dynamical behavior of Gauss-Seidel type finite cellular automata, Mem. Fac. Sci. Kyushu Univ. Ser.A, Vol.47 (1993) 15-26.
  4. Yamamoto, N. and Nakao, M.T. : Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains, Numer. Math. Vol.65 (1993) 503-521.
  5. Yamamoto, N. and Nakao, M.T. : Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element, J. Comput. Appl. Math., Vol.60 (1995) 271-279.
  6. Watanabe, Y., Yamamoto, N. and Nakao, M.T. : Verified computations of solutions for nondifferentiable elliptic equations related to MHD equilibria, Nonlinear Anal., Theory, Method & Appl., Vol.28 (1997) 577-587.
  7. Nakao, M.T., Yamamoto, N. and Kimura, S. : On the best constant in the error bound for the H10-projection into piecewise polynomial spaces, J. Approx. Theory, Vol.93 (1998) 491-500.
  8. Nakao, M.T. and Yamamoto, N. : Numerical verification of solutions for nonlinear elliptic problems using an Linfty residual method, J. Math. Anal. Appl., Vol.217 (1998) 246-262.
  9. Nakao, M.T. and Yamamoto, N. and Watanabe, Y. : A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations, J. Comput. Appl. Math., Vol.91 (1998) 137-158.
  10. Nakao, M.T. and Yamamoto, N. and Watanabe, Y. : Constructive L2 error estimates for finite element solutions of the Stokes equations, Reliab. Comput., Vol.4 (1998) 115-124.
  11. Yamamoto, N. : A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed point theorem, SIAM J. Numer. Anal., Vol.35 (1998) 2004-2013.
  12. Nakao, M.T., Yamamoto, N. and Nagatou, K. : Numerical verifications for eigenvalues of second-order elliptic operators, Japan J. Indust. Appl. Math., Vol.16 (1999) 307-320.
  13. Nagatou, K., Yamamoto, N. and Nakao, M.T. : An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness, Numer. Funct. Anal. Optim., Vol.20 (1999) 543-565.
  14. Watanabe, Y., Yamamoto, N. and Nakao, M.T. : A numerical verification method of solutions for the Navier-Stokes equations, Reliab. Comput., Vol.5 (1999) 347-357.
  15. Watanabe, Y., Yamamoto, N., Nako, M.T. : Verification methods of generalized eigenvalue problems and its applications, Transaction of the Japan Society for Industrial and Applied Mathematics, Vol.9 (1999) 137-150. (In Japanese)
  16. Kimura, S. and Yamamoto, N. : On explicit bounds in the error for the H10-projection into piecewise polynomial spaces, Bull. Inform. Cybernet., Vol.31 (1999) 109-116.
  17. Minamoto, T., Yamamoto, N. and Nakao, M.T. : Numerical verification method for solutions of the perturbed Gelfand equation, Methods Appl. Anal., Vol.7 (2000) 251-262.
  18. Yamamoto, N. : A simple method for error bounds of eigenvalues of symmetric matrices, Linear Algebra and its Applications, Vol.324 (2001) 227-234.
  19. Nakao, M.T., Yamamoto, N. : A guaranteed bound of the optimal constant in the error estimates for linear triangular element, Computing Supplementum, Vol.15 (2001) 165-173.
  20. Nakao, M.T., Watanabe, Y. and Yamamoto, N. : Verified numerical computations for an inverse elliptic eigenvalue problem with finite data, Japan J. Indust. Appl. Math., Vol.18 (2001) 587-602.
  21. Yamamoto, N. and Hayakawa, K. : Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains, J. Comput. Appl. Math., 159 (2003) 173-183.
  22. Nakao, M.T. Watanabe, Y., Yamamoto, N. and Nishida, T. : Some computer assited proofs for solutions of the heat convection problems, Reliable Computing, Vol.9 (2003) 359-372.
  23. Watanabe, Y., Yamamoto, N., Nakao, M.T. and Nishida, T. : A numerical verification of nontrivial solutions for the heat convection problems, J. Math. Fluid Mech., Vol.6 (2004) 1-20.
  24. Yamamoto, N., Matsuda, N. : Validated computation for Bessel functions with multiple-precision arithmetic, Transaction of the Japan Society for Industrial and Applied Mathematics, Vol.15,N0.3 (2005) 347-359. (In Japanese)
  25. Watanabe, Y.,Yamamoto, N., Nakao,M.T. : An efficient approach to the numerical verification for solutions of elliptic differential equations with local uniqueness, Transaction of the Japan Society for Industrial and Applied Mathematics, Vol.15,N0.4 (2005) 509-520. (In Japanese)
  26. Yamamoto, N., Genma, K. : On error estimation of finite element approximations to the elliptic equations in nonconvex domains, J. Comput. Appl. Math., 199 (2007) 286-296.
Proceedings:
  1. Nakao, M.T. and Yamamoto, N. : Numerical verification of solutions for elliptic problems by the residual methods, Proceedings of the 1st China-Japan Seminar on Numerical Mathematics, Beijing, 1993.
  2. Nakao, M.T. and Yamamoto, N. : A simplified method of numerical verification for nonlinear elliptic equations, International Symposium on Nonlinear Theory and its Applications (NOLTA '95), 263-266, Las Vegas, 1995.
  3. Nakao, M.T., Yamamoto, N., Watanabe, Y. : Guaranteed error bounds for finite element solutions of the Stokes problem, Scientific Computing and Validated Numerics, G. Alefeld et al. edited, Akademie Verlag, 1996.
  4. Nakao, M.T., Yamamoto, N. and Nishiura, Y. : Numerical verification of the solution curve for some parametrized nonlinear elliptic problem, Proceedings of Third China-Japan Seminar on Numerical Mathematics, 238-245, Science Press. Beijing, 1998.
  5. Yamamoto, N., Nakao, M.T. and Watanabe, Y. : Validated computation for a linear elliptic problem with a parameter, Advances in Numerical Mathematics; Proceedings of the Fourth Japan-China Joint Seminar on Numerical Mathematics, 155-162, GAKUTO Internat. Ser. Math. Sci. Appl. 12, Gakkotosho, Tokyo, 1999.
  6. Nakao, M.T. and Yamamoto, N. : A guaranteed bound of the optimal constant in the error estimates for linear triangular element, Part II: Details, Perspectives on enclosure methods (Karlsruhe, 2000), 265-276, Springer, Vienna, 2001.
Computational Science