Local representation of functions of D variables by means of discrete orthogonal polynomials

✍ Scribed by K. Helfrich

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 157 KB
• Volume: 20
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(80)90108-3

✦ Synopsis

Discrete normalized orthogonal polynomials ofD variables are defined by means of the orthogonal polynomials of a discrete variable introduced by Tchebychef. If a function of D variables is given by its values on a mesh, it may easily be expanded into a series of these polynomials of D variables. A truncation of this expansion is optimal in the sense of the method of least squares. The expansion may be used to study properties of the original function such as local extrema.