Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence

Abstract

We show that SIESTA, the simplest iterative extension of the Sturm/Triggs algorithm, descends an error function. However, we prove that SIESTA does not converge to usable results. The iterative extension of Mahamud et al. has similar problems, and experiments with "balanced" iterations show that they can fail to converge. We present CIESTA, an algorithm which avoids these problems. It is identical to SIESTA except for one extra, simple stage of computation. We prove that CIESTA descends an error and approaches fixed points. Under weak assumptions, it converges. The CIESTA error can be minimized using a standard descent method such as Gauss-Newton, combining quadratic convergence with the advantage of minimizing in the projective depths.