Pitfalls in the use of computers for the Newton-Raphson method

Extract

It is generally accepted that the presentation of numerical methods will depend to a large extent on the type of student being taught. Mathematics students should be exposed to error analysis and possible pitfalls of the various techniques. However, other groups of students, such as engineers or physicists, usually require a different approach, and the emphasis tends to be more on showing how to use the method on a calculator or, preferably, a computer. Indeed, at Napier College, students are encouraged to write their own programs and/or use the microcomputer laboratory. This practice, though commendable, does have the danger that the students begin to believe every answer that the computer/calculator generates. They forget that rounding errors can become important, and in fact teachers often forget to mention this, since more than 8 figure accuracy can always be assumed.