Related papers: Old and new algorithms for pi
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two…
Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…
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…
When a pair of non-incident edges of a tetrahedron is chosen, the midpoints of the remaining 4 edges are the vertices of a planar parallelogram. A formula is given in terms of the six edge lengths for the area of this parallelogram. It is…
We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of $\mathbb{Z}^d$ supercritical Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T.…
A 1979 letter from John Tate to Jean-Pierre Serre in which the author describes an efficient and elegant algorithm for computing local heights on elliptic curves.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We show that a straightforward rewrite of a known minimal polynomial algorithm yields a simpler version of a recent algorithm of A. Salagean.
In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant…
Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.
A lattice Delaunay polytope P is called perfect if its Delaunay sphere is the only ellipsoid circumscribed about P. We present a new algorithm for finding perfect Delaunay polytopes. Our method overcomes the major shortcomings of the…
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
For some $\epsilon > 10^{-36}$ we give a randomized $3/2-\epsilon$ approximation algorithm for metric TSP.
In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…
We present a new recursion and Hamiltonian operators for the Viallet equation. This new recursion operator and the recursion operator found in [Theoretical and Mathematical Physics, 167:421--443 (2011), arXiv:1004.5346] satisfy the elliptic…
A re-calculation of a known family of formulas of PI is carried out, revisiting the old Archimedes' algorithm. This allows to identify a general family equation and three new simple formulas of Pi in terms of the golden ratio PHI in the…
We derive a simple efficient algorithm for Abelian periods knowing all Abelian squares in a string. An efficient algorithm for the latter problem was given by Cummings and Smyth in 1997. By the way we show an alternative algorithm for…
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.
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…