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Interlacing zeros and divided differences
Russian Mathematical Surveys, 2004The communication under review deals with the construction of sequences which alternate or preserve its sign. Two theorems generalize well known facts as that stated for polynomials with real simple zeros for which the signs of the critical values alternate. Let \(H=\{h_1,\dots ,h_n\} \) be a complete Chebyshev system on the interval \(I\), and let \(X=
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Divided Differences and Combinatorial Identities
Studies in Applied Mathematics, 1991We present an algebraic theory of divided differences which includes confluent differences, interpolation formulas, Liebniz's rule, the chain rule, and Lagrange inversion. Our approach uses only basic linear algebra. We also show that the general results about divided differences yield interesting combinatorial identities when we consider some suitable
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Root finding by divided differences
Numerische Mathematik, 1981A recursive method is presented for computing a simple zero of an analytic functionf from information contained in a table of divided differences of its reciprocalh=1/f. A good deal of flexibility is permitted in the choice of ordinate and derivative values, and in the choice of the number of previous points upon which to base the next estimate of the ...
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The Divided Central Differences of Zero
Canadian Journal of Mathematics, 1963PutIn a recent paper (4), Lohne showed ...
Carlitz, Leonard, Riordan, John
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An adaptive divided-difference perturbation method for solving stochastic problems
Structural Safety, 2023Feng Wu +4 more
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Positive expressions for skew divided difference operators
, 2014For permutations $$v,w \in \mathfrak S_n$$v,w∈Sn, Macdonald defines the skew divided difference operators $$\partial _{w/v}$$∂w/v as the unique linear operators satisfying $$\partial _w(PQ) = \sum _v v(\partial _{w/v}P) \cdot \partial _vQ$$∂w(PQ)=∑vv(∂w ...
Ricky Ini Liu
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Interpolation and divided differences
2002Abstract The problem that we consider in this chapter is the following: let f be a function which we assume to be continuous on the interval [a, b] and let xO, xl,... , xn be n + 1 pairwise distinct points given in the interval [a, b].
Michelle Schatzman, John Taylor
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ON AN INEQUALITY FOR DIVIDED DIFFERENCES
Asian-European Journal of Mathematics, 2008The main purpose of this paper is to give the generalization and improvement of the result given in [2] on the inequality of the difference of two integral means which can also be represented as the difference of two divided differences.
Pečarić, Josip, Rodić, Mirna
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The iterated divided difference filter
2008 IEEE International Conference on Automation and Logistics, 2008With an application to target tracking, the iterated divided difference filter is presented. In new algorithm, an iterated measurement update was proposed to improve the approximation accuracy of the nonlinear state estimation. When iterating, the current mean and the covariance of the divided difference filter (DDF) were used to measurement update ...
null Yong Shi +2 more
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Blossoming and Divided Difference
2001Blossoming and divided difference are shown to be characterized by a similar set of axioms. But the divided difference obeys a cancellation postulate which is not included in the standard blossoming axioms. Here the blossom is extended to incorporate a new set of parameters along with a cancellation axiom.
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