# Linear Interpolation

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## linear interpolation

[′lin·ē·ər in‚tər·pə′lā·shən]
(mathematics)
A process to find a value of a function between two known values under the assumption that the three plotted points lie on a straight line.

## 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 x0 and x1 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 x2 of the root α the point of intersection of the line passing through the points (x0, f(x0)) and (x1, f(x1)) and the x-axis (see Figure 1).

Figure 1

Repeating this procedure on a smaller interval [x0, x2], we find the next approximations x3, and so on. The approximation xn 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.
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