Sampling Exactly from the Normal Distribution
- MathematicsACM Trans. Math. Softw.
An algorithm for sampling exactly from the normal distribution that reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same base with mean cost that scales linearly in the precision.
Zeros of the digamma function and its Barnes G-function analogue
ABSTRACT The zeros of the digamma function are known to be simple and real, but up to now few identities involving them have appeared in the literature. By establishing a Weierstrass infinite product…
P-finite Recurrences From Generating Functions with Roots of Polynomials
We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such…
Code Generators for Mathematical Functions
- Computer Science2015 IEEE 22nd Symposium on Computer Arithmetic
This article suggests to replace this libm paradigm by a more general approach: the on-demand generation of numerical function code, on arbitrary domains and with arbitrary accuracies, which opens up the libm function space available to programmers.
The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries
- Computer ScienceNetwork Science
The network structure of Wikipedia, MathWorld, and DLMF is studied from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web.
Certified counting of roots of random univariate polynomials
- Computer Science, MathematicsArXiv
This work combines an efficient multiprecision implementation for solving high-degree random polynomials with two certification methods, namely Smale's $\alpha$-theory and Gerschgorin's theorem, for showing that a given numerical approximation is in the quadratic convergence region of Newton's method of some exact solution.
Infinitely Divisible Distributions and Commutative Diagrams
We study infinitely divisible (ID) distributions on the nonnegative half-line R+. The Lévy-Khintchine representation of such distributions is well-known. Our primary contribution is to cast the…
Faster Algorithms via Approximation Theory
- Computer ScienceFound. Trends Theor. Comput. Sci.
This monograph presents techniques to approximate real functions such as xs; x—1 and e—x by simpler functions and shows how these results can be used for the design of fast algorithms. The key lies…
A Study of L-Functions: At The Edge of the Critical Strip and Within
In analytic number theory, and increasingly in other surprising places, L-functions arise naturally when describing algebraic and geometric phenomena. For example, when attempting to prove the Prime…
Evaluation of Statistic Probability Distribution Functions: I. Computation of the Standard Normal z, Student's t, F, and Chi-Squared Values
- Mathematics2016 International Conference on Computational Science and Computational Intelligence (CSCI)
Evaluation of probability distribution functions and their inverse functions play a central role in finding a critical value or threshold for a statistical inference and analysis. A polynomial…
SHOWING 1-10 OF 15 REFERENCES
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
A handbook of mathematical functions that is designed to provide scientific investigations with a comprehensive and self-contained summary of the mathematical functions that arise in physical and…
Solving equations exactly
The problem of the solution of a given se t of lin ear equations Ax = b on a high-speed digital computer has been studied intensively, and there are a large number of method s, more or less sati…
Numerical solution of second-order linear difference equations
A ne w al~orilhm is ~ive n fur cumpulin ~ Ihe soluliun of a ny secu nd-orde r lin ea r diffe re nce e qua lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau se uf…
Asymptotics and Special Functions
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
Lowan , The Computation Laboratory of the National Bureau of Standards , Scripta Math
Digital Library of Mathematical Functions, (http://dlmf.nist.gov) National Institute of Standards and Technology
- Digital Library of Mathematical Functions, (http://dlmf.nist.gov) National Institute of Standards and Technology
Y1(x), K0(x), K1(x) 0< = x< = 1
- Y1(x), K0(x), K1(x) 0< = x< = 1