Definition:Interpolation

Definition

Let $f$ be a real function.

Let $y_1, y_2, \ldots, y_n$ be known values of $f$ corresponding to $x_1, x_2, \ldots, x_n$ respectively.

Interpolation is the process of estimating a value $y'$ of $f$ for a value $x$ lying somewhere between $2$ of the values of $x$ whose images are known.

Linear Interpolation

Linear interpolation is a form of interpolation in which it is assumed that $\tuple {x_i, y_i}$, $\tuple {x', y'}$ and $\tuple {x_{i + 1}, y_{i + 1} }$ all lie on the same straight line.

Also see

• Lagrange Interpolation Formula
• Definition:Gregory-Newton Interpolation

• Definition:Extrapolation

• Results about interpolation can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): interpolation
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): numerical analysis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): interpolation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): numerical analysis