What are orthogonal polynomials with respect to a weight, Basic Computer Science

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What are orthogonal polynomials with respect to a weight

1. What are orthogonal polynomials with respect to a weight function w(x)? Why are they useful for numerical computations?

2. What are the Legendre polynomials, and how can they be used to solve the continuous least squares problem?

3. Describe how to compute a best approximation on a general interval, [a,b], not necessarily equal to the interval [-1,1].

4. Explain what trigonometric polynomials are. Are they really polynomials? Are they orthogonal?

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Basic Computer Science: What are orthogonal polynomials with respect to a weight

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