Chapter 12
Gauss for Linear Systems
In Chapter 5, we studied linear systems of two equations in two unknowns. A whole chapter for such a humble task seems like a bit of overkill—its main purpose was really to lay the groundwork for this chapter.
Linear systems arise in virtually every area of science and engineering—some are as big as 1,000,000 equations in as many unknowns. Such huge systems require more sophisticated treatment than the methods introduced here. They will allow you to solve systems with several thousand equations without a problem.
Figure 12.1 illustrates the use of linear systems in the field of data smoothing. The left triangulation looks somewhat “rough”; after setting up an appropriate linear system, we compute the “smoother” ...
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