Related papers: Old and new algorithms for pi
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
We develop a simple and efficient algorithm for approximating the John Ellipsoid of a symmetric polytope. Our algorithm is near optimal in the sense that our time complexity matches the current best verification algorithm. We also provide…
In "Octonion Algebra and its Connection to Physics" [16] an algorithm on octonions is brought forward for description of physical law, the "octonion variance sieve process". This paper expresses the used algorithm in symbolic form, and…
In this paper, an outlier elimination algorithm for ellipse/ellipsoid fitting is proposed. This two-stage algorithm employs a proximity-based outlier detection algorithm (using the graph Laplacian), followed by a model-based outlier…
This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
The present paper deals with the generalization of Midpoint Ellipse Drawing Algorithm (MPEDA) to minimize the error in the existing MPEDA in cartesian form. In this method, we consider three different values of h, i.e., 1, 0.5 and 0.1. For…
We obtained a new formula for $\pi$.
This article concerns the results obtained in [Cabr\'e, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)], which established the H\"older regularity of stable solutions to semilinear elliptic equations in the optimal range of dimensions…
The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(n\log{n})$…
This paper describes a new alignment algorithm for sequences that can be used for determination of deletions and substitutions. It provides several solutions out of which the best one can be chosen on the basis of minimization of gaps or…
We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new…
The formulas discussed in the previous version are not new.
We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide…
In this paper we revisit a result due to Franz Rellich on smoothness of solutions of parametrized linear systems. With this result as a starting point, we obtain finer smoothness results in an elementary fashion and propose an efficient…
In this article we use theoretical and numerical methods to evaluate in a closed-exact form the parameters of Ramanujan type $1/\pi$ formulas.
We present a new extensive analysis of the old problem of finding a satisfactory calibration of the relation between the geometric albedo and some measurable polarization properties of the asteroids. To achieve our goals, we use all…
This is the revised version of a Comment on a paper by C. Escudero (Phys. Rev. Lett. 100, 116101, 2008; arXiv:0804.1898).
Newman-Janis algorithm for Kerr-Newman geometry is reanalyzed in the light of Cartan calculus.
This article discusses how the automation of tensor algorithms, based on A Mathematics of Arrays and Psi Calculus, and a new way to represent numbers, Unum Arithmetic, enables mechanically provable, scalable, portable, and more numerically…