Convergence Analysis of the Algorithm in "Efficient and Robust Discrete Conformal Equivalence with Boundary"

TL;DR

This paper proves that a specific Newton algorithm with line search for discrete conformal equivalence converges quadratically, providing theoretical assurance of its efficiency.

Contribution

It offers a rigorous convergence proof for the Newton algorithm used in discrete conformal equivalence problems, enhancing understanding of its performance.

Findings

The Newton algorithm converges quadratically.

The convergence proof applies to the algorithm with line search.

The result improves theoretical understanding of the method.

Abstract

In this note we prove that the version of Newton algorithm with line search we used in [2] converges quadratically.