Error bounds for the method of simultaneous projections with infinitely many subspaces (Q2054274)

Here authors investigate the properties of the simultaneous projection method as applied to countably infinitely many closed and linear subspaces of a real Hilbert space. They establish the optimal error bound for linear convergence of this method, which is expressed in terms of the cosine of the Friedrichs angle computed in an infinite product space. In addition, authors provide estimates and alternative expressions for the above-mentioned number. They also relate this number to the dichotomy theorem and to super-polynomially fast convergence. Polynomial convergence of the simultaneous projection method which takes place for particularly chosen starting points is also discussed.