Fast Verified Solutions of Sparse Linear Systems with H-matrices. - Atsushi Minamihata; Kouta Sekine; Takeshi Ogita; Shin'ichi Oishi (Reliab. Comput., 2013)

Numerical verification of positiveness for solutions to semilinear elliptic problems. - Kazuaki Tanaka; Kouta Sekine; Makoto Mizuguchi; Shin'ichi Oishi (JSIAM Lett., 2015)

Sharp numerical inclusion of the best constant for embedding on bounded convex domain. - Kazuaki Tanaka; Kouta Sekine; Makoto Mizuguchi; Shin'ichi Oishi (J. Comput. Appl. Math., 2017)

Techniques Concerning Computation Accuracy. - Shin'ichi Oishi; Yusuke Morikura; Kouta Sekine; Hisayasu Kuroda; Maho Nakata (The Art of High Performance Computing for Computational Science, Vol. 1, 2019)

A new formulation for the numerical proof of the existence of solutions to elliptic problems. - Kouta Sekine; Mitsuhiro T. Nakao; Shin'ichi Oishi (CoRR, 2019)

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. - Kouta Sekine; Mitsuhiro T. Nakao; Shin'ichi Oishi (Numerische Mathematik, 2020)

Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation. - Makoto Mizuguchi; Mitsuhiro T. Nakao; Kouta Sekine; Shin'ichi Oishi (J. Sci. Comput., 2021)

Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems. - Kouta Sekine; Kazuaki Tanaka; Shin'ichi Oishi (Comput. Math. Appl., 2022)