Rehabilitation of the Gauss-Jordan Algorithm.
Remarks on addition processes of positive floating-point numbers
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
Roundoff Analysis and Sparse Data.
Round-Off Error Analysis of Iterations for Large Linear Systems.
Round-off error analysis of the gradient method