## Wynn.jl

Wynn's Epsilon Algorithm for transforming symbolic SymPy expressions
Author J-Revell
Popularity
3 Stars
Updated Last
3 Years Ago
Started In
March 2019

# Wynn.jl

A package to facilitate the calculation of epsilon ( ) table structures, derived from Wynn's recursive epsilon algorithm. The components of the epsilon table are commonly used within the calculation of sequence transformations.

Wynn's epsilon algorithm computes the following recursive scheme: ,

where

The resulting table of values is known as the epsilon table. Epsilon table values with an even -th index, i.e. , are commonly used to compute rational sequence transformations and extrapolations, such as Shank's Transforms, and Pade Approximants.

# Example usage: computing the epsilon table for exp(x)

The first 5 terms of the Taylor series expansion for are . The epsilon table can be generated in the manner below:

```using SymPy
using Wynn
# or, if not registered with package repository
# using .Wynn

@syms x
# first 5 terms of the Taylor series expansion of exp(x)
s = [1, x, x^2/2, x^3/6, x^4/24]

etable = EpsilonTable(s).etable```

Retrieving the epsilon table value corresponding to is done by

`etable[i, j]`

Alternatively, the same term can be calculated without generating the entire epsilon table using the `epsilon` function which is much more efficient.

`epsilon(s, (i, j))`

## Further usage: computing the R[2/2] Pade Approximant of exp(x)

`R = etable[0,4]`

which yields It can be seen that as x moves away from 0, the Pade approximant is more accurate than the corresponding Taylor series.

### Used By Packages

No packages found.