Insertion algorithm for inverting the signature of a path

2019/07/19 by Terry Lyons, Chang, Jiawei, Lyons, Terry · 1 citation
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Polynomial and algebraic computation #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1907.08423

Abstract

In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the inserted n-th term and the (n+1)-th term of the normalised signature of a smooth path, and we also show that there exists a constant lower bound for a subsequence of the terms in the normalised signature of a piecewise linear path. We demonstrate our results with numerical examples.

Cited by

• SL₂(R)-developments and Signature Asymptotics for Planar Paths with Bounded Variation

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