Overview

orthogonal functions


More Like This

Show all results sharing this subject:

  • Computing

GO

Show Summary Details

Quick Reference

Let

f1(x), f2(x),…, fn(x)

be a set of functions defined on the interval (a,b); also let w(x) be a given positive function (a weight function) on (a,b). The functions fi(x),

i = 1,2,…,n

are said to be orthogonal with respect to the interval (a,b) and weight function w(x), if

baw(x) fi(x)fj(x) dx = 0,

ij, i,j = 1,2,…,n

If, for i = j,

abw(x) fi2(x) dx = 1,

i = 1,2,…,n

then the functions are said to be orthonormal.

A similar property is defined when (a,b) is replaced by the set of points

x1,x2,…,xn

and the integral is replaced by a sum,

ij

Orthogonal functions play an important part in the approximation of functions and data.

Subjects: Computing.


Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.