A fast algorithm for the construction of recurrence relations for modified moments
A new approach is presented for constructing recurrence relations for the modified moments of a function with respect to the Gegenbauer polynomials.
A fast floating-point square-rooting routine for the 8080/8085 microprocessors
A matrix analysis of the stability of the Clenshaw algorithm.
A Modified Fast Fourier Transform for Polynomial Evaluation and the Jenkins-Traub Algorithm.
A new modulo computation algorithm
A relationship between the modified Euler method and e.
Algorithm 1. Elliptic integrals of the second and third kinds
Algorithm 12. Minimum of a function of one variable
Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values
2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...
Algorithms in Unnormalized Arithmetic. II. Unrestricted Polynomial Evaluation.
An analytical method for calculation of integrals appearing in approximate solutions of deformable body mechanics
An approximation for the zeros of Bessel functions.
Analytic Representations Suitable for Numerical Computation of Some Special Functions.
Approximation of elliptic integrals of the third kind for large values of argument and modulus
Are the coefficients of a polynomial well-conditioned functions of its roots?
Avoiding look-ahead in the Lanczos method and Padé approximation
In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for...
Bessel Transforms and Rational Extrapolation.
Calculation of the Complete Elliptic Integrals with Complex Modulus.
Cálculo rápido de las funciones de Bessel modificadas Kis(X) e Iis(X) y sus derivadas.
En este trabajo discutimos la resolución de la ecuación de Besseld2x/dx2 + (1/x)(dy/dx) - (1 - s2/x2)y = 0.Las funciones de Bessel modificadas Kv(x) e Iv(x) son las soluciones a la ecuación anterior cuando v = is. El valor de la función Kis(x) es real y el de la función Iis(x) es complejo, por ello definimos en su lugar una función real Mis(x). La función Iis(x) resultará ser una combinación de las funciones Kis(x) y Mis(x). Daremos algunos desarrollos en serie de Mis(x) y Kis(x) junto con sus derivadas...
Computing Elliptic Integrals by Duplication.