Solving Simultaneous Equations
In Chapter 4, numerical techniques for a single equation, f (x) = 0, were discussed. In this chapter, numerical methods for solving a set of simultaneous equations are explained. Many problems in engineering and science end up with solving a set of linear simultaneous equations after they are discretized and linearized. Solving a set of simultaneous equations is one of the most important subjects in numerical analysis. If you took a linear algebra course, you must have learned Cramer’s rule which expresses the solution to linear simultaneous equations using the determinants of matrices. However, Cramer’s rule is limited to 2 and 3 simultaneous equations and in real-world applications, it ...