Schaum's Outline of Numerical Analysis

Rating:
Summary: useful revision of many numerical methods
Review: Scheid gives us a broad range of methods in numerical analysis. The 846 problems can certainly keep you busy. Plus, the book is also useful as a concise summary of the most common and useful methods in the field. Students of maths, physical sciences and engineering should already be familiar with several of the methods. Like performing numerical integration or differentiation, because these mathematical steps are the fundamental calculus operations, and those fields all use these. So too is finding roots of equations, and for this, there is a chapter on Newton's method. Which tends to assume that you have an analytic form for the function and for its derivative, where you want the roots of the function.

The book also supports statistics. Unsurprisingly, since statistics is inherently about numerical evaluations. So we have least squares methods of curve fitting, and Monte Carlo methods, where the latter can also be used for numerical integration.

Ironically, while the Monte Carlo is described, the book is somewhat weak on methods for generating random numbers. And how to measure the "randomness" of such algorithms. For this, I suggest you turn to "The Art of Computer Programming" by Donald Knuth. He has an excellent length discussion on the subject.

Curve fitting is also discussed in a chapter on splines. You may already be acquainted with these, in the context of graphics packages which can fit B splines to data points.