Let $$T_n$$ be the linear Hadamard convolution operator acting over Hardy space $$H^q$$ , $$1\le q\le \infty $$ . We call a best approximation-preserving (BAP operator) if $$T_n(e_n)=e_n$$ where $$e_n(z):=z^n,$$ and $$\Vert T_n(f)\Vert _q\le E_n(f)_q$$ for all $$f\in H^q$$ $$E_n(f)_q$$ is approximation by algebraic polynomials of degree most $$n-1$$ in space. give necessary sufficient condition...

The Reeb space, which generalizes the notion of a Reeb graph, is one of the few tools in topological data analysis and visualization suitable for the study of multivariate scientific datasets. First introduced by Edelsbrunner et al. [3], the Reeb space of a multivariate mapping f : X→ R parameterizes the set of components of preimages of points in R. In this paper, we formally prove the converg...

Given a function f 2 L2(Q), Q := [0, 1)2 and a real number t > 0, let U( f , t) := infg2BV (Q) kf gkL2(I) + t VQ (g), where the infimum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for finding ...

Combining classical line geometry with techniques from numerical approximation, we develop algorithms for approximation in line space. In particular, linear complexes, linear congruences and reguli are tted to given sets of lines or line segments. The results are applied to computation-ally robust detection of special robot conngurations and to reconstruction of fundamental surface shapes from ...

multi-criteria shortest path problems (mspp) are called as np-hard. for mspps, a unique solution for optimizing all the criteria simultaneously will rarely exist in reality. algorithmic and approximation schemes are available to solve these problems; however, the complexity of these approaches often prohibits their implementation on real-world applications. this paper describes the development ...