Improving the speed of convergence in the method of projections onto convex sets. (English) Zbl 0973.65001

This paper is concerned with the method of projections onto convex sets, which is suited to solve the problem of finding the intersection of a finite number of closed convex sets in an \(m\)-dimensional Euclidean space. A serious drawback of the method is the slow convergence due to the so-called “tunneling effect” that seems connected with the monotone behavior of the usual algorithms. The author presents a method which improves the convergence speed in those cases where the tunneling effect is strong and keeps an acceptable speed of convergence in other cases. The convergence of the new algorithm is discussed, illustrated for some examples, and compared for different starting points to the method of pure projections and to the parallel method.


65B99 Acceleration of convergence in numerical analysis
65J15 Numerical solutions to equations with nonlinear operators