# Linear Interpolation

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## linear interpolation

[′lin·ē·ər in‚tər·pə′lā·shən]## Linear Interpolation

a method of approximating the roots of a transcendental or algebraic equation *f*(x) = 0.

The essence of the method of linear interpolation consists in the following. Starting with two values *x*_{0} and *x*_{1} that are close to the root α and at which the values of the function *f*(x) have opposite signs, we take as the next approximate value *x*_{2} of the root α the point of intersection of the line passing through the points (*x*_{0}, *f*(*x*_{0})) and (*x*_{1}, *f*(*x*_{1})) and the *x*-axis (see Figure 1).

Repeating this procedure on a smaller interval [*x*_{0}, *x*_{2}], we find the next approximations *x*_{3}, and so on. The approximation *x _{n}* is given by the formula

Other names for the linear interpolation method are the method of chords, the method of secants, and the rule of false position (*regula falsi*), the last being obsolete.

### REFERENCE

Berezin, I. S., and N. P. Zhidkov.*Metody vychislenii*, 2nd ed., vol. 2. Moscow, 1962.