Legendre Polynomials The Legendre polynomials form an -orthogonal set of polynomials. You will see below why orthogonal polynomials make particularly good choices for approximation. In this section, we are going to write m-files to generate the Legendre polynomials and we are going to confirm that they form an orthogonal set in . Throughout this section, we will be representing polynomials as vectors of coefficients, in the usual way in Matlab. The Legendre polyonomials are a basis for the set of all polynomials, just as the usual monomial powers of are. They are appropriate for use on the interval [-1,1] because they are orthogonal when considered as members of . Polynomials that are orthogonal are discussed by Quarteroni, Sacco, and Saleri in Chapter 10, with Legendre polynomials discussed in Section 10.1.2. The first few Legendre polynomials are:
Legendre Polynomials matlab: