Computing the $\sin_{p}$ function via the inverse power method

TL;DR

This paper introduces an iterative inverse power method for efficiently computing the $ ext{sin}_p$ function, which is linked to nonlinear eigenvalue problems of the $p$-Laplacian, offering a competitive alternative to existing methods.

Contribution

The paper presents a novel iterative approach inspired by the inverse power method to compute $ ext{sin}_p$, enhancing computational efficiency for nonlinear eigenvalue problems.

Findings

Method is competitive with existing algorithms.

Provides a new tool for nonlinear eigenvalue computations.

Improves efficiency in calculating $ ext{sin}_p$.

Abstract

In this paper, we discuss a new iterative method for computing $\sin_{p}$. This function was introduced by Lindqvist in connection with the unidimensional nonlinear Dirichlet eigenvalue problem for the $p$-Laplacian. The iterative technique was inspired by the inverse power method in finite dimensional linear algebra and is competitive with other methods available in the literature.