False Position Method

The false position method or regula falsi method is a term for problem-solving methods in arithmetic, algebra, and calculus. In simple terms, these methods begin by attempting to evaluate a problem using test ("false") values for the variables, and then adjust the values accordingly.

Two basic types of false position method can be distinguished, simple false position and double false position. Simple false position is aimed at solving problems involving direct proportion. Such problems can be written algebraically in the form: determine x such that

,

if a and b are known. Double false position is aimed at solving more difficult problems that can be written algebraically in the form: determine x such that

,

if it is known that

.

Double false position is mathematically equivalent to linear interpolation; for an affine linear function,

,

it provides the exact solution, while for a nonlinear function f it provides an approximation that can be successively improved by iteration.