Sentence examples for a divided difference from inspiring English sources

where V is a divided difference.

From Ostrowski's scheme adding one step of Newton with 'frozen' derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems.

In order to prove Theorem 3, the following complete monotonic properties of a function related to a divided difference of the psi function were discovered in [54], the preprint of [55].

By using a particular divided difference of first order we can transform many iterative methods into derivative-free iterative schemes, holding the order of convergence of the departure original method.

In order to estimate position and velocity error of the spacecraft and reduce the impact of the system noise on navigation precision, an adaptive divided difference filter (ADDF) is applied.

In the paper [24] Daletskii and Krein proved that in the case when the self-adjoint operator A is bounded for nice functions f the map (tmapsto f(A+tK)) has m-th derivative and it can be expressed in terms a multiple operator integral whose integrand is a higher order divided difference of f.

A th-order divided difference of at distinct points is defined recursively by (51).

Finally, we mention a representation of the divided difference by means of two determinants.

Definition 6 The second-order divided difference of a function f : [ a, b ] → R at mutually distinct points y 0, y 1, y 2 ∈ [ a, b ] is defined recursively by (23).

holds for every α, β ∈ ℝ and x, y ∈ I. Definition 2. The second order divided difference of a function f : [a, b] → ℝ at mutually different points y0, y1, y2 ∈ [a, b] is defined recursively by (18).

Note that the divided difference is a permutation symmetric function.