TABLE OF CONTENTS Given the pace of technology, I propose we leave math to the machines and go play outside.
- CALVIN, Calvin and Hobbes by Bill Watterson (1992)
To analyse a given numerical algorithm we proceed as follows. A number which measures the effect of roundoff error is assigned to each set of data. "Hill-climbing" procedures are then applied to search for values large enough to signal instability.
- WEBB MILLER, Software for Roundoff Analysis (1975)
The prospects for effective use of interval arithmetic look very good, so efforts should be made to increase its availability and to make it as user-friendly as possible.
- DONALD E. KNUTH, The Art of Computer Programming, Volume 2, Seminumerical Algorithms (1998)
Despite its wide use, until quite recently the Nelder-Mead method and its ilk have been deprecated, scorned, or ignored by almost all of the mainstream optimization community.
- MARGARET H. WRIGHT, Direct Search Methods: Once Scorned, Now Respectable (1996)
Automatic error analysis is any process in which we use the computer to help us analyse the accuracy or stability of a numerical computation. The idea of automatic error analysis goes back to the dawn of scientific computing. For example, running error analysis, described in 3.3, is a form of automatic error analysis; it was used extensively by Wilkinson on the ACE machine. Various forms of automatic error analysis have been developed. In this chapter we describe in detail the use of direct search optimization for investigating questions about...
