We introduce majorant computability of functions on reals. A structural theorem is proved, which connects the graph of a majorant{computable function with validity of a nite formula on the set of the hereditarily nite set HF( R) (where R is an elementary proper extension of standard real numbers). The class of majorant{computable functions in our approach include an interesting class of real to...

Characteristic properties of majorant-computable real-valued functions are studied. A formal theory of computability over the reals which satisses the requirements of numerical analysis used in Computer Science is constructed on the base of the deenition of majorant-computa-bility proposed in 13]. A model-theoretical characterization of majorant-computability real-valued functions and their dom...

We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s Method, the relationship of the majorant function and the non-linear operator under consideration. This approach enable us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new...

We prove that a positive function on the unit disk admits a harmonic majorant if and only if a certain explicit upper envelope of it admits a superharmonic majorant. We provide examples to show that mere superharmonicity of the data does not help with the problem of existence of a harmonic majorant. 1. Definitions and statements Let D stand for the open unit disk in the complex plane, and H(D) ...

We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements o...

This article discusses the generation of temperature majorant cross sections, the type of cross sections required by two separate techniques related to Monte Carlo neutron tracking, namely the Doppler-broadening rejection correction (DBRC) and Target Motion Sampling (TMS) temperature treatment methods. In the generation of these cross sections the theoretically infinite range of thermal motion ...

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above ...

In this paper new fundamental theorems are stated, which allow to easily determine a first-order majorant system of a pseudo-quadratic uncertain MIMO discrete-time system. For the above class of systems, some results and systematic methods are provided, which allow to solve, “via majorant system”, several analysis problems of robust stability, stabilization and tracking of a generic reference s...

We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with ...