B. Otero, J.M. Cela, and E. Fontdecaba (Spain)
Global bases, optimization, symmetric indefinite
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 , , 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 ill
conditioning 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 ill
conditioning 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.