Search results
Results From The WOW.Com Content Network
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
Schemes defined for scattered data on an irregular grid are more general. They should all work on a regular grid, typically reducing to another known method. Nearest-neighbor interpolation; Triangulated irregular network-based natural neighbor; Triangulated irregular network-based linear interpolation (a type of piecewise linear function)
One good solution is linear interpolation, which draws a line between the two points in the table on either side of the value and locates the answer on that line. This is still quick to compute, and much more accurate for smooth functions such as the sine function. Here is an example using linear interpolation:
The original use of interpolation polynomials was to approximate values of important transcendental functions such as natural logarithm and trigonometric functions.Starting with a few accurately computed data points, the corresponding interpolation polynomial will approximate the function at an arbitrary nearby point.
For that purpose, the divided-difference formula and/or its x 0 point should be chosen so that the formula will use, for its linear term, the two data points between which the linear interpolation of interest would be done. The divided difference formulas are more versatile, useful in more kinds of problems.
Multilinear polynomials are the interpolants of multilinear or n-linear interpolation on a rectangular grid, a generalization of linear interpolation, bilinear interpolation and trilinear interpolation to an arbitrary number of variables. This is a specific form of multivariate interpolation, not to be confused with piecewise linear
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression , including variants for ordinary (unweighted), weighted , and generalized (correlated) residuals .