Abstract: Paper is devoted to the development of a method for approximating discontinuous functions by discontinuous splines and the construction of an algorithm for detecting discontinuity lines. The ...

ABSTRACT: This paper investigates four classes of functions with a single discontinuous point. We give the sufficient and necessary conditions under which the second order iterates are continuous ...

For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by ...

There are many scientific problems related to the topic of interpolation, especially for non-‎continuous functions, as well as the evaluating of the integrals of such non-continuous ‎‎functions. These ...

In this paper the existence of one-sided filters is proved for spectral Fourier approximations of discontinuous functions, which can recover spectral accuracy up to the discontinuity from one side. A ...

ABSTRACT: In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a ...

Abstract: Our goal is addressing the problems of preassigned-time projective synchronization and fixed-time projective synchronization of the system that studied in our article, and fuzzy terms, mixed ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...