Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Yoshitaka Watanabe Last modified date:2022.04.18

Associate Professor / Section of Advanced Computational Science / Research Institute for Information Technology


Papers
1. Shuting Cai, Yoshitaka Watanabe, Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem, Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2021.113603, 395, 113603, 2021.11, 2次元Navier-Stokes方程式に特別な外力項を課したKolmogorov問題に対し、その2次分岐点にあたる対称性破壊分岐点が真に存在することを、計算機援用証明によって具体的な誤差評価付きで明らかにした。.
2. Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, Some improvements of invertibility verifications for second-order linear elliptic operators, Applied Numerical Mathematics, 10.1016/j.apnum.2020.03.016, 154, 36-46, 2020.08, This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L2-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported..
3. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2019.112561, 369, 112561, 2020.05, This paper presents some lower estimates for resolvents of a compact operator A on an infinite-dimensional Hilbert space. Usually, upper estimates for resolvents are known under suitable conditions but lower estimates are not known. These estimates enable us to calculate suitability results for approximation of a resolvent..
4. Shuting Cai, Yoshitaka Watanabe, A computer-assisted method for the diblock copolymer model, ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 10.1002/zamm.201800125, 99, 7, 2019.07, We propose a computer-assisted method by which to enclose a solution of the diblock copolymer model. We begin by using the Newton method to obtain a solution, and we then prove that the residual part of the approximation is a fixed point of a compact operator. Next, using a computer, we construct a set which satisfies the hypothesis of the Banach fixed-point theorem for the operator in a certain Sobolev space, which therefore contains a unique solution. Finally, we present some verified results..
5. Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-019-00344-8, 2019.01, This paper presents an improved method for determining the invertibility of second-order linear elliptic operators with a bound on the norm of their inverses by computers in a mathematically rigorous sense. This approach is an improvement on a previous method (Nakao et al. in Jpn J Ind Appl Math 32:19–32, 2015) which used a projection and constructive a priori error estimates. Several examples confirming the effectiveness of the proposed procedure are reported..
6. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces, Journal of Differential Equations , 10.1016/j.jde.2018.10.027, 266, 9, 5431-5447, 2019.04, In the present paper, we propose a computer-assisted procedure to prove the invertibility of a linear operator in a Hilbert space and to compute a verified norm bound of its inverse. A number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates. The approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications. Several verification examples that confirm the actual effectiveness of the proposed procedure are reported..
7. Yoshitaka Watanabe, Mitsuhiro T. Nakao, and Kaori Nagatou, On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations, JSIAM Letters, doi.org/10.14495/jsiaml.9.77, 9, 77-80, 2017.12.
8. Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao, Validated constructive error estimations for biharmonic problems, Reliable Computing, 25, 168-177, 2017.08.
9. Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao, Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-016-0223-y, 33, 3, 629-636, 2016.12.
10. Yoshitaka Watanabe, An Efficient Numerical Verification Method for the Kolmogorov Problem of Incompressible Viscous Fluid, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2016.01.055, 302, 157-170, 2016.09.
11. Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Norm Bound Computation for Inverses of Linear Operators in Hilbert Spaces, Journal of Differential Equations , 10.1016/j.jde.2015.12.041, 260, 7, 6363-6374, 2016.04, 無限次元Hilbert空間における線形作用素に対し、可逆性の保証と逆作用素ノルムの具体的な上界値を数学的に厳密な意味で計算機で与える一般理論を構築するとともに、与えた上界が最適な作用素ノルムに収束することを明らかにしました。さらに、具体的な問題に対する計算機援用証明により、その有効性を明らかにしました.
12. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators, Scientific Computing, Computer Arithmetic, and Validated Numerics; 16th International Symposium, SCAN 2014, Würzburg, Germany, September 21-26, 2014. Revised Selected Papers (M. Nehmeier, J. Wolff von Gudenberg, W. Tucker, eds.), Lecture Notes in Computer Science, 10.1007/978-3-319-31769-4_18, 9553, 225-235, 2016.04.
13. Yoshitaka Watanabe, Mitsuhiro T. Nakao, A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration, Applied Mathematics and Computation, doi:10.1016/j.amc.2015.12.021, 276, 239-251, 2016.03, 無限次元Hilbert空間の非線形関数方程式に対し、弱形式に基づく残差引き戻しと無限次元Newton法を組み合わせた堅牢な解の存在検証理論を提案し、非線形偏微分方程式を含む具体的な問題に対する計算機援用証明により、その有効性を明らかにしました。.
14. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, Recurrence Relations of Orthogonal Polynomials in H01 and H02, Nonlinear Theory and Its Applications, IEICE, http://doi.org/10.1587/nolta.6.404, 6, 3, 404-409, 2015.07.
15. Shuting Cai, Yoshitaka Watanabe, A Computer-assisted Method for Excluding Eigenvalues of an Elliptic Operator Linearized at a Solution of a Nonlinear Problem, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-015-0167-7, 32, 1, 263-294, 2015.03.
16. Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takehiko Kinoshita, Takuma Kimura, Nobito Yamamoto, Some Considerations of the Invertibility Verifications for Linear Elliptic Operators, Japan Journal of Industrial and Applied Mathematics, 10.1007/s13160-014-0160-6 , 32, 1, 19-32, 2015.03.
17. Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao, Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces, SIAM Journal on Numerical Analysis, 10.1137/120894683, 52, 2, 975-992, 2014.05, 無限次元Hilbert空間における複素数固有値問題の固有値の数学的に厳密な非存在範囲を与える一般定理と、具体的な非存在領域を求めるための精度保証付き数値計算アルゴリズムを提案するとともに、丸め誤差の影響を考慮した具体的な数値例を確認可能なプログラムコードとともに与えた。.
18. Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao, An Improvement of the Theorem of A Posteriori Estimates for Inverse Elliptic Operators, Nonlinear Theory and Its Applications, IEICE, 5, 1, 47-52, 2014.01.
19. Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao, A Posteriori Estimates of Inverse Operators for Boundary Value Problems in Linear Elliptic Partial Differential Equations, Mathematics of Computation, 82, 283, 1543-1557, 2013.07.
20. Yoshitaka Watanabe, A Simple Numerical Verification Method for Differential Equations Based on Infinite Dimensional Sequential Iteration, Nonlinear Theory and Its Applications, IEICE, 4, 1, 23-33, 2013.01.
21. Shuting Cai, Kaori Nagatou, Yoshitaka Watanabe, A Numerical Verification Method for a System of FitzHugh-Nagumo Type, Numerical Functional Analysis and Optimization, 33, 10, 1195-1220, 2012.10.
22. Toshio Sakata, Kazumitsu Maehara, Takeshi Sasaki, Toshio Sumi, Mitsuhiro Miyazaki, Yoshitaka Watanabe, Makoto Tagami, Tests of Inequivalence Among Absolutely Nonsingular Tensors Through Geometric Invariants, Universal Journal of Mathematics and Mathematical Sciences, 1, 1, 1-28, 2012.01.
23. Nobito Yamamoto, Mitsuhiro T. Nakao, Yoshitaka Watanabe, A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations, Numerical Functional Analysis and Optimization, 32, 11, 1190-1204, 2011.11, Nobito Yamamoto, Mitsuhiro T. Nakao, and Yoshitaka Watanabe:.
24. Mitsuhiro T. Nakao, and Yoshitaka Watanabe, Numerical Verification Methods for Solutions of Semilinear Elliptic Boundary Value Problems, Nonlinear Theory and Its Applications, 2, 1, 2-31, 2011.01.
25. Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, and Mitsuhiro T. Nakao, A Computer-assisted Stability Proof for the Orr-Sommerfeld Problem with Poiseuille Flow, Nonlinear Theory and Its Applications, IEICE, 2, 1, 123-127, 2011.01.
26. Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida and Myoung-Nyoun Kim, Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems, Journal of Scientific Computing, 43, 3, 388-401, 2000.07.
27. Yoshitaka Watanabe and Mitsuhiro T. Nakao, Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh-Bénard Problem, Japan Journal of Industrial and Applied Mathematics, 26, 2-3, 443-463, 2009.10.
28. Yoshitaka Watanabe, A Numerical Verification Method for Two-Coupled Elliptic Partial Differential Equations, Japan Journal of Industrial and Applied Mathematics, 26, 2-3, 233-247, 2009.10.
29. Yoshitaka Watanabe, Michael Plum, Mitsuhiro T. Nakao , A computer-assisted instability proof for the Orr-Sommerfeld problemwith Poiseuille flow, Journal of Applied Mathematics and Mechanics (ZAMM), Vol.89, No.1, 5-18, 2009.01.
30. Yoshitaka Watanabe, A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid, Journal of Computational and Applied Mathematics, Vol.223, pp.953-966., 2009.01.
31. Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe and Takaaki Nishida, A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Be\'nard problems, Numerische Mathematik, Vol.111, No.3, pp.389-406, 2009.01.
32. 渡部 善隆, Michael Plum, 中尾 充宏, 並行Poiseuille流れの不安定性に対する計算機援用証明, 京都大学数理解析研究所講究録, Vol.1614 (2008) pp.11-19., 2008.11.
33. Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto and Takaaki Nishida, A numerical verification of bifurcation points for nonlinear heat convection problems, The proceedings of 2nd International conference "From Scientific Computing to Computational Engineering" (2nd IC-SCCE), 8pages, 2006.07.
34. 渡部 善隆, Some computer assisted proofs on the bifurcation structure of solutions for the Rayleigh-Bénard problem, 京都大学数理解析研究所講究録, Vol.1536, pp.87-96., 2007.02.
35. Takeshi Nanri, Yoshitaka Watanabe, Hiroyuki Sato, Performance comparison of vector-calculations between Itanium2 and other processors, Proceedings of International Workshop on Innovative Architecture, pp. 141-146, 2006.01.
36. Kouji Hashimoto, Ryohei Abe, Mitsuhiro T. Nakao and Yoshitaka Watanabe, A Numerical Verification Method for Solutions of Singularly Perturbed Problems with Nonlinearity, Japan Journal of Industrial and Applied Mathematics, 22, 1, 111-131, Vol.22, No.1, pp.111-131, 2005.03.
37. Mitsuhiro T. Nakao, Kouji Hashimoto and Yoshitaka Watanabe, A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems, Computing, 10.1007/s00607-004-0111-1, 75, 1, 1-14, Vol.75, Number 1, pp.1-14, 2005.07.