ABSTRACT
The next three chapters form the central portion of this volume, in particular Chapter 10, which defines the approximate iterative algorithm (AIA) on Banach and Hilbert spaces, and establishes the main convergence results. Following this, Chapter 11 considers the problem of determining the optimal design of an AIA when approximation tolerances can be controlled. In such cases, it can be advantageous to start the AIAwith a coarse approximation, which would reduce computation cost, gradually refining the approximation as the iterations proceed. The precise convergence rates derived in Chapter 10 can be used to determine near optimal rates of approximation refinement, the problem considered in Chapter 11.
