A modified algorithm for accurate inverse Cholesky factorization

Yuka Yanagisawa, Takeshi Ogita, Shin'ichi Oishi

Nonlinear Theory and Its Applications 5(1) 34-46 2014

Fast verified solutions of sparse linear systems with H-matrices

A. Minamihata, K. Sekine, T. Ogita, S. Oishi

Reliable Computing 2014

Remarks on computable a priori error estimates for finite element solutions of elliptic problems

A. Takayasu, X. Liu, S. Oishi

Nonlinear Theory and its Applications, IEICE. 5(1) 53-63 2014

An algorithm of identifying parameters satisfying a sufficient condition of Plum's Newton-Kantorovich like existence theorem for nonlinear operator equations

K. Sekine, A. Takayasu, S. Oishi

Nonlinear Theory and its Applications, IEICE. 5(1) 64-79 2014

Fast Quadruple-double Floating Point Format

N. Yamanaka, S. Oishi

Nonlinear Theory and its Applications, IEICE. 51(1) 15-34 2014

Our research group is composed of scholars working in the areas of discrete mathematics, nonlinear differential equations, information theory and numerical computation. We have organized "Seminar on Digital Analysis" so that members can hold commo...

Establishment of Verified Numerical Computation We have studied verified numerical computations for partial differential equations and systems of linear equations using digital computers. Calculating sum of a vector and dot product of two vectors ...

Development of computer assisted analysis for complicated nonlinear phenomena

We were working on the development and applications of the numerical verification methods for solutions of nonlinear partial differential equations, in particular, we succeeded in finding a new and very efficient verification principle for nonline...

Synthetic approach for the development of computer assisted analysis from the numerical verification methods

In this research, we newly developed the numerical verification methods which can be applied to wide mathematical and analytical problems, as well as extended or improved the existing techniques.And we actually applied these methods to particular ...

Synthetic approach for new developments of self-validating numerics

In this research, we newly developed the self-validating numerical methods which can be applied to wide mathematical and analytical problems as well as extended or improved the existing techniques.And we actually applied these methods to particula...