interpolación

Interpolación is a mathematical technique used to estimate unknown values that fall within a range of known data points. It is commonly employed in various fields such as science, engineering, and data analysis to smooth data, fill in missing values, or create continuous functions from discrete data points. The process involves constructing new data points within the range of a discrete set of known data points.

There are several methods of interpolation, each with its own advantages and limitations. Linear interpolation is the simplest form, where a straight line is drawn between two known points to estimate the value at an intermediate point. This method is efficient but may not be suitable for data that exhibits significant curvature or variability.

Polynomial interpolation extends linear interpolation by fitting a polynomial curve through multiple data points. This approach can provide a more accurate representation of the data, especially when the relationship between the variables is non-linear. However, it can lead to oscillations and inaccuracies, known as the Runge phenomenon, when higher-degree polynomials are used.

Spline interpolation is another popular method that uses piecewise polynomial functions to create a smooth curve that passes through or closely approximates the known data points. Cubic splines, in particular, are widely used due to their balance of accuracy and computational efficiency.

Interpolation is a fundamental tool in data analysis and modeling, enabling the creation of continuous functions from discrete data and facilitating the estimation of unknown values. However, it is important to choose the appropriate interpolation method based on the characteristics of the data and the specific requirements of the application to ensure accurate and reliable results.