Significance of orthogonal polynomials

[lonewolf219]

Two polynomials are considered orthogonal if the integral of their inner product over a defined interval is equal to zero... is that a correct and complete definition? From what I understand, orthogonal polynomials form a basis in a vector space. Is that the desirable quality of orthogonal polynomials? Do they have any other additional properties that set them apart?

 

[rcgldr]

They can be used to simplify least squares curve fitting (no matrix inversion) for higher order polynomials.

http://rcgldr.net/misc/opls.rtf

 

[lonewolf219]

Thanks rcgldr. Is it safe to say that orthogonal polynomials are continuous?

 

[AlephZero]

All polynomials are continuous functions

But there are non-polynomial orthogonal functions which are not continuous, for example Haar and Walsh functions.

 

[lonewolf219]

Great! Thanks AlephZero!