Chebyshev Expansions for Solutions of Linear Differential Equations
Alexandre Benoit (INRIA Rocquencourt), Bruno Salvy (INRIA, Rocquencourt)

TL;DR
This paper explores Chebyshev expansions for solving linear differential equations, analyzing existing algorithms and proposing a faster method for computing solutions using recurrence relations.
Contribution
It introduces a novel interpretation of recurrence relations as fractions of linear operators, enabling improved algorithmic efficiency for high-order solutions.
Findings
New interpretation of recurrence equations as operator fractions
Complexity analysis of existing algorithms
Development of a faster algorithm for large orders
Abstract
A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
