Definition:Rule of False Position/Double Position

Definition

The method of double position is a category of the rule of false position in which two estimates $a_0$ and $b_0$ are made such that $\map f {a_0}$ and $\map f {b_0}$ are both close to zero but of opposite sign.

These estimates are then used as starting values in the formula:

$a_{n + 1} = a_n - \dfrac {\paren {b_n - a_n} \map f {a_n} } {\map f {b_n} - \map f {a_n} }$

where, for $n = 0, 1, 2, \ldots$, $b_{n + 1}$ is chosen from $a_n$ and $b_n$ so that $\map f {b_{n + 1} }$ is of opposite sign to $\map f {a_{n + 1} }$.

Also see

• Definition:Linear Interpolation

• Results about the rule of false position can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): false position (rule of) (regula falsi)${}$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): false position, rule of (regula falsi)