Related papers: Old and new algorithms for pi
This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavour than the original analytic…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We proposed an algorithm that covers some cases of Hamilton Circuit Problem.
We comment upon a numerical computation in a recent paper by Balasubramanian, Buchel, Green, Lehner, and Liebling.
This paper formalize the existence's proof of first-integrals for any second order ODE, allowing to discriminate periodic orbits. Up to the author's knowledge, such a powerful result is not available in the literature providing a tool to…
I think the title and content of the recent Letter by Georgeot and Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As long as the classical Arnold map is considered, the classical computational algorithm can be…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
The article is devoted to the issue of the polar form of octonions. This is a~continuation of the works initiated by Hahn and Snopek in their articles from 2011. The results presented in the article show errors made in previous…
In 1948, Fritz John proposed a theorem stating that every convex body has a unique maximal volume inscribed ellipsoid, known as the John ellipsoid. The John ellipsoid has become fundamental in mathematics, with extensive applications in…
In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we…
This is a Reply to the Comment of S.R. White and D.J. Scalapino [cond-mat/9907243] on our recent paper ``Stripes and the t-J Model'' [Physical Review Letters 83, 132 (1999) and cond-mat/9812022].
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
In a recent paper, Byun presented nice formulas for the enumeration of lozenge tilings of certain hexagonal regions with intrusions. This paper attempts to generalise some of Byun's investigations.
We present a new proof of a recent $\epsilon$ regularity of G. Tian and J.Viaclovsky. Moreover, our idea also also works with a kind of $L^p, p<\dim M/2$ assumptions on the curvature.
We design a randomized algorithm that finds a Hamilton cycle in $\mathcal{O}(n)$ time with high probability in a random graph $G_{n,p}$ with edge probability $p\ge C \log n / n$. This closes a gap left open in a seminal paper by Angluin and…
As the spherical object can be seen everywhere, we should extract the ellipse image accurately and fit it by implicit algebraic curve in order to finish the 3D reconstruction. In this paper, we propose a new ellipse fitting algorithm which…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
The paper is written for Kluwer's Encyclopaedia of Mathematics.