Ad
related to: sequence of transformations examples questions
Search results
Results From The WOW.Com Content Network
The binomial transform and the Stirling transform are two linear transformations of a more general type. An example of a nonlinear sequence transformation is Aitken's delta-squared process, used to improve the rate of convergence of a slowly convergent sequence. An extended form of this is the Shanks transformation. The Möbius transform is ...
Examples of such nonlinear sequence transformations are Padé approximants, the Shanks transformation, and Levin-type sequence transformations. Especially nonlinear sequence transformations often provide powerful numerical methods for the summation of divergent series or asymptotic series that arise for instance in perturbation theory , and ...
The remainder of the results and examples given in this section sketch some of the more well-known generating function transformations provided by sequences related by inversion formulas (the binomial transform and the Stirling transform), and provides several tables of known inversion relations of various types cited in Riordan's Combinatorial ...
In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely related to the Euler transform, which is the result of applying the binomial transform to the sequence associated with its ordinary generating function.
The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it ...
For example, the transfer operator is defined in terms of the pushforward of the transformation map ; the measure can now be understood as an invariant measure; it is just the Frobenius–Perron eigenvector of the transfer operator (recall, the FP eigenvector is the largest eigenvector of a matrix; in this case it is the eigenvector which has ...
In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. [1] It is most useful for accelerating the convergence of a sequence that is converging linearly.
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.