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An efficient algorithm is presented for computation of the limit of exp(t A) for t towards infinity where A denotes an intensity matrix of finite dimension.

Classical Analysis and ODEs · Mathematics 2025-01-10 Helmut Kahl

We give a simple algorithm for the construction of the tight span of a finite subset of the Manhattan plane.

Metric Geometry · Mathematics 2016-03-07 Mehmet Kılıç , Şahin Koçak , Yunus Özdemir

We describe an algorithm for listing all elements of bounded height in a given number field.

Number Theory · Mathematics 2021-08-12 John R. Doyle , David Krumm

We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…

Symbolic Computation · Computer Science 2018-01-08 Ming-Shing Chen , Chen-Mou Cheng , Po-Chun Kuo , Wen-Ding Li , Bo-Yin Yang

A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…

Cryptography and Security · Computer Science 2015-04-07 Igor Semaev

In this paper, we give a fast algorithm for the computation of the Arf closure of an algebroid curve with more than one branch, generalizing an algorithm presented by Arslan and Sahin for the algebroid branch case.

Commutative Algebra · Mathematics 2018-05-29 Nicola Maugeri , Giuseppe Zito

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's quantity $A(\ell)$, for $\ell = p^n$ with $p$…

Algebraic Geometry · Mathematics 2013-05-21 Alp Bassa , Peter Beelen , Arnaldo Garcia , Henning Stichtenoth

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

Algebraic Geometry · Mathematics 2020-06-09 Alain Couvreur , Philippe Lebacque , Marc Perret

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…

Probability · Mathematics 2007-06-13 Mikhail Kovtun , Igor Akushevich , Kenneth G. Manton , H. Dennis Tolley

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…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate…

Fluid Dynamics · Physics 2012-02-24 Doug Lipinski , Kamran Mohseni

A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…

Numerical Analysis · Mathematics 2012-05-07 Irenee Briquel , Felipe Cucker , Javier Pena , Vera Roshchina

Algorithms for the computation of geodesics on an ellipsoid of revolution are given. These provide accurate, robust, and fast solutions to the direct and inverse geodesic problems and they allow differential and integral properties of…

Geophysics · Physics 2013-01-08 Charles F. F. Karney

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence.…

Optimization and Control · Mathematics 2020-04-14 Heinz H. Bauschke , Minh N. Dao

Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for…

Number Theory · Mathematics 2026-03-13 Laura Capuano , Sara Checcoli , Marzio Mula , Lea Terracini

We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…

Dynamical Systems · Mathematics 2014-08-15 Yury Kroll , Boris Mirman

We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.

Mathematical Physics · Physics 2009-10-31 G. G. Athanasiu , E. G. Floratos , S. Nicolis

This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…

Symbolic Computation · Computer Science 2017-07-12 Sven Puchinger , Antonia Wachter-Zeh

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…

Data Structures and Algorithms · Computer Science 2009-09-30 Clemence Magnien , Matthieu Latapy , Michel Habib

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…

Mathematical Software · Computer Science 2010-06-03 Norbert Th. Müller , Margarita Korovina