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2. Series acceleration - Wikipedia

   en.wikipedia.org/wiki/Series_acceleration

   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 ...

3. List of transforms - Wikipedia

   en.wikipedia.org/wiki/List_of_transforms

   Affine transformation (Euclidean geometry) Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression) Chirplet transform; Distance transform; Fractal transform; Gelfand transform; Hadamard transform; Hough transform (digital image processing) Inverse scattering transform; Legendre ...

4. Sequence transformation - Wikipedia

   en.wikipedia.org/wiki/Sequence_transformation

   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 ...

5. Aitken's delta-squared process - Wikipedia

   en.wikipedia.org/wiki/Aitken's_delta-squared_process

   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.

6. Silverman–Toeplitz theorem - Wikipedia

   en.wikipedia.org/wiki/Silverman–Toeplitz_theorem

   The linear sequence transformation can be applied to the divergent sequences of partial sums of divergent series to give those series generalized sums. An infinite matrix ( a i , j ) i , j ∈ N {\displaystyle (a_{i,j})_{i,j\in \mathbb {N} }} with complex -valued entries defines a regular matrix summability method if and only if it satisfies ...

7. Series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Series_(mathematics)

   Partial summation of a sequence is an example of a linear sequence transformation, and it is also known as the prefix sum in computer science. The inverse transformation for recovering a sequence from its partial sums is the finite difference , another linear sequence transformation.

8. Operator (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Operator_(mathematics)

   The most important cases are sequences of real or complex numbers, and these spaces, together with linear subspaces, are known as sequence spaces. Operators on these spaces are known as sequence transformations. Bounded linear operators over a Banach space form a Banach algebra in respect to the standard

9. Linear map - Wikipedia

   en.wikipedia.org/wiki/Linear_map

   A specific application of linear maps is for geometric transformations, such as those performed in computer graphics, where the translation, rotation and scaling of 2D or 3D objects is performed by the use of a transformation matrix. Linear mappings also are used as a mechanism for describing change: for example in calculus correspond to ...