Gaussian Quadrature and the Eigenvalue Problem
نویسنده
چکیده
where the nodes xk belong to the range of integration and the weights wk are computable. For example, this kind of formula always results when f̂ is a polynomial of degree less than n that interpolates to f at the nodes; i.e., f̂ (xk) = f (xk) for k = 1, . . . ,n. As we show below, once the nodes xk are fixed, it is easy to choose the weights wk so that if f is any polynomial of degree less than n, then ∫ f dμ = n ∑ k=1 wk f (xk).
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