# Iterative Polynomial Approximation Algorithms for Inverse Graph Filters

arXiv: https://arxiv.org/abs/2504.14341 · HTML: https://mlsanity.com/paper/2504.14341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Difference-of-Convex Regularization for Graph Learning by Differentiable Programming](https://mlsanity.com/paper/2608.12757/) (2026)

## Abstract (arXiv)

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm and the conventional gradient descent algorithm do.