On the semilocal convergence of a fast two-step Newton method.
On the Stability of Finite Numerical Procedures.
On total truncation error estimation for the one-step method
In this paper the author establishes estimation of the total truncation error after steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.
Optimal Approximation and Error Bounds in Seminormed Spaces.
Parallel Interval Multisplittings.
Perturbation of parallel asynchronous linear iterations by floating point errors.
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
Set arithmetic and the enclosing problem in dynamics
We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
Solution of a system of linear equations with given error sets for coefficients
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Solution-bounds for a class of difference equations
Spolehlivost numerických výpočtů
Square-root families for the simultaneous approximation of polynomial multiple zeros.
Stability of Fast Algorithms for Matrix Multiplication.
Stochastic Arithmetic Theory and Experiments
Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing...
Teilbarkeitskriterien der Intervallarithmetik.