PAD&APPROXIMANTS FOR THE SOLUTION OF A SYTEM OF NONLINEAR EQUATIONS ANNIE Cm-T? and PAUL VAN DER CRUYSSEN University of Antwerp, Department of Mathematics, Universiteitsplein 1, B-2610 Wihijk, Belgium (Receioed January 1981; and in revised form May 1982) Communicated by J. F. Traub Abstract-Let F: R4 *R’ and let x* be a simple root of the system of nonlinear equations F(x) = 0. We will construc...

The variable fractional-delay (FD) filter structure by Tassart and Depalle performs Lagrange interpolation in an efficient way. We point out that this structure directly corresponds to Newton’s interpolation (backward difference) formula, hence we prefer to refer to it as the Newton FD filter. This structure does not function correctly when the fractional delay is made time-variant, e.g., in sa...

A new algorithm for rational interpolation is proposed. Given the data set, the algorithm generates a set of orthogonal polynomials by the classical threeterm recurrence relation and then uses Newton interpolation to find the numerator and the denominator polynomials of the rational interpolating function. The number of arithmetic operations of the algorithm to find a particular rational interp...

The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...

Pad6 approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives of f ( x 1 .... ,xp). Therefore multivariate Newton-Pad6 approximants are introduced; their computation will only use the value of f at some points. In Sect. 1 we shall repeat the univariate Newton-Pad6 ap...

This report presents several approaches aimed at reducing the bias and uncertainty of the free energy difference estimates obtained using the thermodynamic integration simulation strategy. The central idea is to utilize interpolation schemes, rather than the often-used trapezoidal rule quadrature, to fit the thermodynamic integration data, and obtain a more accurate and precise estimate of the ...