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

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.