The adjective 'interpolatory' describes something that involves or relates to interpolation. Interpolation, in mathematics and other fields, is the process of estimating the value of a function between known values. This often involves creating a new data point within the range of a discrete set of known data points. 'Interpolatory' methods aim to find a curve or surface that passes through a given set of points, allowing estimations for unknown values within that defined data space. The applications are broad, including curve fitting, data smoothing, and the creation of continuous representations from discrete samples. The accuracy of an interpolatory method often depends on the number and distribution of the known data points and the choice of interpolation technique.
Interpolatory meaning with examples
- The scientist used an interpolatory method to predict the population size between the census years, using the known values from the decennial counts. The model generated a smooth curve, showing the estimated growth rate. The interpolation allowed for valuable predictions.
- In computer graphics, the shader employs interpolatory techniques to determine the color values across the pixels of a polygon, producing a smooth visual appearance based on the vertex colors. This provides a high-quality visual result.
- The engineer employed an interpolatory algorithm to create a complete model of the terrain, given a number of surveyed elevation points. The model used these existing points to smoothly represent the unseen areas in the terrain, for use by others.
- The data analysis project required the use of an interpolatory scheme to fill the missing data values in the sensor readings. The system predicted the values in a reliable manner, and filled the gaps in the data.
- During the numerical simulation, an interpolatory function was used to define the pressure at the locations throughout the simulation grid, creating a smooth gradient from known pressure boundary conditions. This was important.