منابع مشابه
On divided-di¤erence semigroups
The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...
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Tools for computational differentiation transform a program that computes a numerical function F(x) into a related program that computes F ′(x) (the derivative of F). This paper describes how techniques similar to those used in computational-differentiation tools can be used to implement other program transformations—in particular, a variety of transformations for computational divided differen...
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Amultivariate kth divided difference is proposed and shown to lead to new error formulæ for polynomial interpolation on some standard multivariate point sets. §
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The main aim of this paper is the development of suitable bases (replacing the power basis x (n ∈ N≥0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2011
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196711006121