Different Surface Models for Progressive Lenses and their Effect in Parallelization

We are interested in diminishing the aberrations in the lateral zones of a progressive lens. In order to achieve this, it is necessary to resolve a nonlinear optimization problem. In previous work [8], [9], this problem was modeled using bases with local control, particularly using Cubic B-Splines. However, the use of these bases in the model generates ill-conditioned problems. The illconditioning of the matrices makes the optimization process long and, in some cases, impossible to carry out. For this reason, we made modifications in the representation of the lens surface, improving the illconditioning of the matrix, and reducing the number of iterations of the optimization process. The proposed modification consists of using bases with global control, specifically polynomials in the canonical base. This work shows the results obtained when the problem is changed. Indeed, the version with and without pivoting of the Modified Cholesky factorization for the global model does not require corrections, and when the original matrix is approximated by a new positive definite matrix, the error is reduced.