1,872 research outputs found
Numerical Recipes: Does This Paradigm Have a Future?
Longtime readers of Computers in Physics may remember us as the editors/authors of the Numerical Recipes column that ran from 1988 through 1992. At that time, with the publication of the second edition of our Numerical Recipes (NR) books in C and Fortran, we took a sabbatical leave from column writing, a leave that became inadvertently permanent. Now, as a part of CIP's Tenth Anniversary celebration, we have been invited back to offer some observations about the past of scientific computing, including the educational niche occupied by our books, and to make some prognostications about where the field is going
Numerical computation of real or complex elliptic integrals
Algorithms for numerical computation of symmetric elliptic integrals of all
three kinds are improved in several ways and extended to complex values of the
variables (with some restrictions in the case of the integral of the third
kind). Numerical check values, consistency checks, and relations to Legendre's
integrals and Bulirsch's integrals are included
Reliability and Statistical Power: How Measurement Fallibility Affects Power and Required Sample Sizes for Several Parametric and Nonparametric Statistics
The relationship between reliability and statistical power is considered, and tables that account for reduced reliability are presented. A series of Monte Carlo experiments were conducted to determine the effect of changes in reliability on parametric and nonparametric statistical methods, including the paired samples dependent t test, pooled-variance independent t test, one-way analysis of variance with three levels, Wilcoxon signed-rank test for paired samples, and Mann-Whitney-Wilcoxon test for independent groups. Power tables were created that illustrate the reduction in statistical power from decreased reliability for given sample sizes. Sample size tables were created to provide the approximate sample sizes required to achieve given levels of statistical power based for several levels of reliability
A fast high-order method to calculate wakefield forces in an electron beam
In this paper we report on a high-order fast method to numerically calculate
wakefield forces in an electron beam given a wake function model. This method
is based on a Newton-Cotes quadrature rule for integral approximation and an
FFT method for discrete summation that results in an computational
cost, where is the number of grid points. Using the Simpson quadrature rule
with an accuracy of , where is the grid size, we present numerical
calculation of the wakefields from a resonator wake function model and from a
one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the
fast speed and high numerical accuracy, the calculation using the direct line
density instead of the first derivative of the line density avoids numerical
filtering of the electron density function for computing the CSR wakefield
force
Accurate numerical potential and field in razor-thin axisymmetric discs
We demonstrate the high accuracy of the density splitting method to compute
the gravitational potential and field in the plane of razor-thin, axially
symmetric discs, as preliminarily outlined in Pierens & Hure (2004).
Because residual kernels in Poisson integrals are not C^infinity-class
functions, we use a dynamical space mapping in order to increase the efficiency
of advanced quadrature schemes. In terms of accuracy, results are better by
orders of magnitude than for the classical FFT-methods.Comment: 11 pages, 5 color figures, 2 table
Geometric Random Inner Products: A New Family of Tests for Random Number Generators
We present a new computational scheme, GRIP (Geometric Random Inner
Products), for testing the quality of random number generators. The GRIP
formalism utilizes geometric probability techniques to calculate the average
scalar products of random vectors generated in geometric objects, such as
circles and spheres. We show that these average scalar products define a family
of geometric constants which can be used to evaluate the quality of random
number generators. We explicitly apply the GRIP tests to several random number
generators frequently used in Monte Carlo simulations, and demonstrate a new
statistical property for good random number generators
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