Overview

Numerical computing means computing with numbers, and the subject is almost as old as civilization itself. Ancient peoples knew techniques to carry out many numerical tasks. Among the oldest computational records that we have is the Egyptian Rhind Papyrus from about 1650 B.C. [Cha79], quoted on the previous page. Counting stones and counting rods have been used for calculation for thousands of years; the abacus originated as a flat surface with counting stones and was used extensively in the ancient world long before it evolved into the device with beads on wires that was common in Asia until recently. The abacus was the basis of calculation in Europe until the introduction of our familiar positional decimal notation from the Middle East, beginning in the 13th century. By the end of the 16th century, positional decimal notation was in standard use throughout Europe, as it became widely recognized for its computational convenience.

The next key development was the invention and tabulation of logarithms by John Napier at the beginning of the 17th century; his idea was that time-consuming multiplication and especially division may be avoided by adding or subtracting logarithms, using tabulated values. Isaac Newton laid the foundations of modern numerical computing later in the 17th century, developing numerical techniques for the solution of many mathematical problems and inventing calculus along the way. Several of Newton's computational methods still bear his name. In Newton's footsteps followed Euler, Lagrange, Gauss, and many other great mathematicians of the 18th and 19th...