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:

You can create estimation plots here at estimationstats.com, or with the DABEST packages which are available in R, Python, and Matlab.

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Integrity Data Attacks in Power Market Operations

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