Search results
Results from the WOW.Com Content Network
This process yields p 0,4 (x), the value of the polynomial going through the n + 1 data points (x i, y i) at the point x. This algorithm needs O(n 2) floating point operations to interpolate a single point, and O(n 3) floating point operations to interpolate a polynomial of degree n.
A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
Use the cell index to access a pre-built lookup table with 16 entries listing the edges needed to represent the cell (shown in the lower right part of the picture below). Apply linear interpolation between the original field data values to find the exact position of the contour line along the edges of the cell.
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.
Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation. It is a fast and efficient method for generating values of functions like the exponential or the trigonometric functions to within last-bit accuracy for almost all argument values without using extended ...
) and the interpolation problem consists of yielding values at arbitrary points (,,, … ) {\displaystyle (x,y,z,\dots )} . Multivariate interpolation is particularly important in geostatistics , where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or ...
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.
When the program requires the sine of a value, it can use the lookup table to retrieve the closest sine value from a memory address, and may also interpolate to the sine of the desired value, instead of calculating by mathematical formula. Lookup tables can thus used by mathematics coprocessors in computer systems.