Numerical Analysis II
Orthogonal polynomials are a sequence of polynomials that are mutually orthogonal with respect to a specific inner product defined on a function space. This property allows them to serve as basis functions in approximation problems, making them particularly useful in spectral methods for solving partial differential equations and in spectral collocation methods for numerical analysis. The orthogonality condition ensures that the polynomials can accurately represent a wide range of functions, leading to efficient convergence in numerical approximations.
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