The current two main methods for computing the numerical are level-set approach of Mengi and Overton cutting-plane method Uhlig, but until now, no formal convergence rate results have been established either. In practice, which is faster also unclear, with Uhlig's sometimes being much than Overton's approach, on other problems, slower. this paper, we clarify issue propose three improved methods...

We develop an algorithm for numerical computation of the Eisenstein series on a Riemann surface of constant negative curvature. We focus in particular on the computation of the poles of the Eisenstein series. Using our numerical methods, we study the spectrum of the Laplace–Beltrami operator as the surface is being deformed. Numerical evidence of the destruction of Γ0(5)-cusp forms is presented.