The automatic computation of second-order slope tuples for some nonsmooth functions.
The Average A Posteriori Error of Numerical Methods.
The eigenvalue problem and Jacobean-like methods for its solution
The uncertainty problem in control theory. I. Models of theories
Thirteen Ways to Estimate Global Error.
Towards a Formal Definition of Numerical Stability.
Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals.
The addition of fuzzy intervals based on a triangular norm T is studied. It is shown that the addition based on a t-norm T weaker than the Lukasiewicz t-norm TL acts on linear fuzzy intervals just as the TL-based addition. Some examples are given.
Truncation Error Analysis by Means of Approximant Systems and Inclusion Regions.
Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions
The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered...
Variable-precision arithmetic considered perilous - a detective story.
Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties
Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical...
Verified numerical computations for large-scale linear systems
This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical solutions....
Weaker convergence conditions for the secant method
We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
Арифметика больших целых чисел на ЭВМ типа M-20
О множестве решений линейного уравнения с интервально заданными оператором и правой частью.
О погрешностях решений линейных алгебраических систем
Об оценке области, содержащей решение системы линейных алгебраических уравнений