We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

We define the notion of a point interaction for general non-self-adjoint elliptic operators in planar domains. show that such can be approximated geometric way by cutting out small cavity around point, at which is concentrated. On boundary cavity, we impose special Robin-type condition with nonlocal term. As shrinks to perturbed operator converges norm resolvent sense limiting one containing an...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

Introduction/purpose: Saddle point approximation has been considered in the paper Methods: The saddle method is used several different fields of mathematics and physics. Several terms expansion for factorial function have explicitely computed. Results: integrals estimated this way values close to exact one. Conclusions: Higher order corrections are not negligible even when requiring moderate le...