Abstract :
Using the results of Smith, Solmon, and Wagner [K. Smith, D. Solomon, S. Wagner, Practical and
mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math.
Soc. 83 (1977) 1227–1270] and Nelson and Neumann [S. Nelson, M. Neumann, Generalizations
of the projection method with application to SOR theory for Hermitian positive semidefinite linear
systems, Numer. Math. 51 (1987) 123–141] we derive new estimates for the speed of the alternating
projection method and its relaxed version in Rm. These estimates can be computed in at most
O(m3) arithmetic operations unlike the estimates in papers mentioned above that require spectral
information. The new and old estimates are equivalent in many practical cases. In cases when the
new estimates are weaker, the numerical testing indicates that they approximate the original bounds
in papers mentioned above quite well.
2005 Elsevier Inc. All rights reserved.
