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Practical Scientific Computing by V Zalizniak, A Muhammad

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7

Solving Nonlinear Equations

Finding a solution for an equation of the form f(x) = 0 is a frequently-encountered problem. It is not as easy to find roots of this equation as it might at first appear. Exact solutions are only possible if f(x) is a polynomial of degree n ≤ 9. By “exact solution,” we mean there is some procedure to calculate a root by using the parameters of the equation (as in the equation ax2 + bx + c = 0). In what follows, the term “root of an equation f(x) = 0” will be used interchangeably with “zero of f(x)”.

The root finding procedure is based on an iterative process or, in other words, on a process of successive approximations. An iterative process has four stages:

1. Root localization – that is, finding an interval which ...

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