Approximating coupled coincidence points by \alpha-dense curves

Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces

and Applied Analysis 3 Definition 2.3. Let X, p be a partial metric space. Then, 1 a sequence {xn} in X, p is called a Cauchy sequence if limn,m→∞p xn, xm exists and is finite ; 2 the space X, p is said to be complete if every Cauchy sequence {xn} inX converges, with respect to τp, to a point x ∈ X such that p x, x limn,m→∞ p xn, xm . Lemma 2.4. Let X, p be a partial metric space. a {xn} is a C...

Fitting Parametric Curves to Dense and Noisy Points

Given a large set of irregularly spaced points in the plane, an algorithm for partitioning the points into subsets and fitting a parametric curve to each subset is described. The points could be measurements from a physical phenomenon, and the objective in this process could be to find patterns among the points and describe the phenomenon analytically. The points could be measurements from a ge...

Approximating fixed points of generalized nonexpansive mappings

Approximating Algebraic Space Curves by Circular Arcs

We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating ci...

Approximating Dense Cases

We study dense cases of several covering problems. An instance of the set cover problem with m sets is dense if there is > 0 such that any element belongs to at least m sets. We show that the dense set cover problem can be approximated with the performance ratio c log n for any c > 0 and it is unlikely to be NP-hard. We construct a polynomial-time approximation scheme for the dense Steiner tree...