Numerical Analysis
Numerical Analysis¶
People often describe Numerical Analysis as being “as much an art as a science”. What they appear to mean by this is that while the results clearly appear to be valuable, they are not altogether sure of how the “artist” decided on the process by which these results were derived, or even the sanity of said “artist’s” thought process. In this course we will try to make these processes clearer and put them on a solid footing. However, it is hard to deny that mastery of Numerical Analysis does require a certain amount of intuition. The best, and really only, way to build this intuition is by using the concepts we will learn about in practical, hands-on problems.
What makes Numerical Analysis different from fields such as computer animation is that we use analysis to ensure that our answer does not just “look right”, but actually is in some quantitative way “close” to the exact result. In fact, it is ideally the exact result of a nearby problem. This requirement of a quantitative analysis of our errors necessitates that we first define a way to measure errors and where they come from, which is the subject of this first chapter.