Results 271 to 280 of about 1,335 (292)

A Remark on Newton's Resistance Formula

ZAMM, 1999
Summary: We consider Newton's model for the resistance of a body in a rarefied gas. A derivation from first principles is given and it is proved that for incompressible fluids the resistance is also given by the Newton functional in leading order.
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On the numerical stability of Newton’s formula for Lagrange interpolation

Journal of Computational and Applied Mathematics, 2020
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Parametric timing estimation with Newton–Gregory formulae

Concurrency and Computation: Practice and Experience, 2006
AbstractThis paper presents a novel method for parametric worst‐case execution time (WCET) estimation of loops. The method determines a parametric bound on the iteration space size of loops with both affine and non‐affine loop bounds in an efficient manner using a formulation based on Newton–Gregory interpolating polynomials.
Robert A. van Engelen, Kyle A. Gallivan, Burt Walsh   +2 more
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A New Variational Result for Quasi-Newton Formulae

SIAM Journal on Optimization, 1991
Summary: The recent measure function of \textit{R. H. Byrd} and \textit{J. Nocedal} [SIAM J. Numer. Anal. 26, 727-739 (1989)] is considered and simple proofs of some of its properties are given. It is then shown that the BFGS and DFP formulae satisfy a least change property with respect to this new measure.
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A Note on a Formula of Newton and an Extension Thereto.

Journal of the Staple Inn Actuarial Society, 1946
Letf(x), f″(x), f″(x)denoteafunction ofx, its first and second derivatives respectively. Iff(x), f″(x)are one-valued, finite and continuous, and f″(x) exists in the neighbourhood of the valueaofx, thenwhere o <θ< I. Suppose the valueais an approximation to a root of the equationf(x)= o, the true value of which isa + h.Equation (I ...
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A unified approach to Newton–Cotes quadrature formulae

Applied Mathematics and Computation, 2003
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A new class of quasi-Newton updating formulas

Optimization Methods and Software, 2008
In this paper, we propose a derivative-free quasi-Newton condition, which results in a new class of quasi-Newton updating formulas for unconstrained optimization. Each updating formula in this class is a rank-two updating formula and preserves the positive definiteness of the second derivative matrix of the quadratic model.
Dong-Hui Li, Liqun Qi 0001, Vera Roshchina   +2 more
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A Newton formula for generalized Berzolari-Radon sets

Advances in Computational Mathematics, 2014
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Jesús M. Carnicer, Carmen Godés
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Analogs of recurrent Newton formulas

Russian Mathematics, 2009
For a system of algebraic equations, the recurrent Newton formulas for evaluating power sums of roots in terms of coefficients are well-known. In this paper, analogs of these formulas are obtained for nonlinear nonalgebraic equations. The main idea is to study sums of negative powers of roots.
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Newton's Formula and the Continued Fraction Expansion of √d

Experimental Mathematics, 2001
It is known that if the period s(d) of the continued fraction expansion of √d satisfies s(d) ≤ 2, then all Newton's approximants are convergents of √d, and moreover Rn = P2n+1/q2n+1 for all n ≥ 0. Motivated by this fact we define j = j(d, n) by Rn = P2n+1+2j/ q2n+1+2j if Rn is a convergent of √d, and define b = b(d) by b = |{n : 0 ≤ n ≤ s-1 and Rn is a
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