Two new approximate algorithms with O ( k l o g k ) for the rectilenear Steiner tree are proposed. Both algorithms base upon the method which makes minimum spanning tree on the modified Delaunay net with the triangular Steiner points as the more virtual generating points, because each point and each edge weight on the modified Delaunay net have been fixed.

An ε-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most ε from each other. Given a set of points and a set of objects, computing the approximate incidences between them is a major step in many database and web-based applications in computer vision and graphics, including robust model fitting,...

In this paper, a pair of generalized nonlinear mappings are introduced. Sufficient conditions for the existence of common fixed points for a pair of generalized nonlinear mappings in convex metric spaces are obtained and Krasnoselskii type iterations are used to approximate common fixed points. Our results generalize and extend various known results. c ©2016 All rights reserved.

Anew approach for creating stable quadrature rules with preassigned points is proposed. The idea is to approximate a known stable quadrature rule by a local interpolation at the preassigned points. The construction cost of the method does not grow as the number of the preassigned points increases. The accuracy of the rule depends only on the accuracy of the chosen stable rule and that of the in...

We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points. These provide new computational tools for polynomial least squares and interpolation on multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.

Approximate computing is a research area where we investigate a wide spectrum of techniques to trade off computation accuracy for better performance or energy consumption. In this work, we provide a general introduction to approximate computing. Also, we propose a taxonomy to make it easier to discuss the merits of different approximation techniques. Our taxonomy emphasizes the expected cost of...

I calculate the top quark forward-backward asymmetry at the Tevatron in both the laboratory frame and the tt̄ rest frame. I show that soft-gluon corrections are the dominant contribution to the asymmetry and closely approximate exact results through next-tonext-to-leading order (NNLO). I present a calculation of the asymmetry including approximate next-to-next-to-next-to-leading-order (N3LO) sof...