MATH 541 NUMERICAL ANALYSIS

CHAPTER 1 OUTLINE

1. ERROR
Absolute error
Relative error
Significant digits

2. TAYLOR'S SERIES
Polynomial evaluation in nested form
Alternating Series truncation error
Cosine Example  MATLAB CODE

3. LOSS OF SIGNIFICANT DIGITS
Subtractive cancellation

An example of loss of significance

Consider the recursion relation x_n+1 = 1 - (n + 1) x_n with x₀ = 1 - 1/e. It can be shown that the sequence defined by this recursion relationship converges to 0. However, subtractive cancellation produces a very large error in this calculation which is approximately equal to the machine precision times n!.  MATLAB CODE

Revised 12/06/04
By Don Short, dshort@sciences.sdsu.edu