Unicity of Best One-Sided L1-Approximations with Applications to Moment Theory and Quadrature Formulae
Let C(I) be the linear space of all real-valued functions defined on I=[0,1] and let G denote an n-dimensional subspace of C(I). First we shall study best one-sided L1-approximation for all functions f in C(I). Existence is readily shown. Therefore we shall concern ourselves with the question of uniqueness. This approximation problem has an important application to numerical integration since it is closely related to the existence and uniqueness of quadrature formulae of highest possible degree of precision (in particular, formulae of Gauss type).
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