ABSTRACT
The "rate of convergence" of an iterative method is of considerable importance, and the study of such rates forms an integral part of numerical analysis. Error analysis plays a major role in this context; sources of errors are manifold and include computer round-off error, errors due to truncations, and errors inherent in mathematical models of physical systems. The chapter focuses on the problem of determining error bounds; the reader should be aware that treatment gives only scant indication of the complexities involved. The use of machines to effect numerical calculations dates back to the work of an Englishman, Charles Babbage, who devoted an extraordinary amount of energy to the construction of a "difference engine." Although this machine was never completed, it would have been capable of performing various mathematical operations and storing information. Babbage's brilliance was duly recognized, but his eccentricities were the subject of even more scrutiny.
