PolyExp
Package for the decomposition of polynomial-exponential series.
Introduction
Sequences $(\sigma_{\alpha})_{\alpha} \in \mathbb{K}^{\mathbb{N}^{n}}$ or series
\[\sigma(y) = \sum_{\alpha \in \mathbb{K}^{\mathbb{N}^{n}}} \sigma_{\alpha} \frac{y^{\alpha}}{\alpha!}\]
which can be decomposed as polynomial-exponential series
\[\sum_{i=1}^r \omega_i(y) e^{\xi_{i,1} y_1+ \cdots + \xi_{i,n} y_n}\]
with polynomials $\omega_{i}(y)$ and points $\xi_{i}= (\xi_{i,1}, \ldots, \xi_{i,n})\in \mathbb{K}^{n}$ appear in many problems (see Examples). The package PolyExp
provides functions to manipulate (truncated) series and to compute such a decomposition from the first terms of the sequence.
Examples
- Weighted sum of Dirac Measures
- Multivariate exponential decompositon
- Sparse interpolation
- Symmetric tensors
- Border basis
Functions and types
Installation
The package is available at https://gitlab.inria.fr/AlgebraicGeometricModeling/PolyExp.jl.
To install it from Julia:
Pkg.clone("https://gitlab.inria.fr/AlgebraicGeometricModeling/PolyExp.jl.git")
It can then be used as follows:
using PolyExp
See the Examples for more details.