Here f(xi) are given values p(xi) that fit exactly at the distinct points xi (compare smoothing). The value of f can be approximated by p(x) for x ≠ xi. In practice p is often a polynomial, linear and quadratic polynomials providing the simplest examples. In addition the idea can be extended to include matching of p′(xi) with f ′(xi); this is Hermite interpolation. The process is also widely used in the construction of many numerical methods, for example in numerical integration and ordinary differential equations. The interpolating polynomial can be represented in many equivalent forms. For example, when the xi are equally spaced, the forward and backward difference forms (see difference equation) are convenient. More commonly, nonequally spaced xi give rise to the divided difference form, which incorporates successive differences (f(xi+1) – f(xi))/(xi+1 – xi), i = 0,1,2,…,n – 1
These are the first divided differences; second divided differences are obtained by a similar differencing process and so on for higher order differences.
"interpolation." A Dictionary of Computing. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/interpolation
"interpolation." A Dictionary of Computing. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/interpolation
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
The process of inserting additional words in a complete document or instrument in such manner as to alter its intended meaning; the addition of words to a complete document or instrument.
Interpolation is synonymous with interlineation.
"Interpolation." West's Encyclopedia of American Law. . Encyclopedia.com. (February 20, 2018). http://www.encyclopedia.com/law/encyclopedias-almanacs-transcripts-and-maps/interpolation
"Interpolation." West's Encyclopedia of American Law. . Retrieved February 20, 2018 from Encyclopedia.com: http://www.encyclopedia.com/law/encyclopedias-almanacs-transcripts-and-maps/interpolation