Synthesis of the Weyl matrix on the square lattice

TL;DR

This paper introduces a step-by-step method for synthesizing the Weyl matrix on square lattices, enabling efficient computation for large graphs and potential extensions to other periodic structures.

Contribution

It presents a novel iterative approach for constructing the Weyl matrix on square lattices, facilitating inverse problem analysis and adaptable to various periodic lattices.

Findings

Efficient synthesis of Weyl matrices for large square lattices.

Method can be extended to other periodic lattice types.

Supports inverse problem studies in lattice structures.

Abstract

A method for successive synthesis of the Weyl matrix on the square lattice is proposed. It allows one to compute the Weyl matrix of a large graph by adding new edges and solving elementary systems of linear algebraic equations at each step. Synthesis of the Weyl matrix is useful to further study the inverse problems of the square lattice. Moreover, our approach can be extended to other types of periodic lattices.