Nonlinear Approximation Theory |
Contents
Preliminaries | 1 |
B Special Function Spaces | 8 |
4 L₁Approximation and Gaussian Quadrature Formulas | 18 |
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algorithm alternant of length approximation problem approximation to f approximatively compact arguments Assume Banach space bounded Braess c₁ C¹-manifold characteristic numbers characterization Chebyshev approximation Chebyshev set consider contains continuous converges convex set critical point defined Descartes E₁ existence set exponential sums f₁ follows given global Haar condition Haar cone Haar subspace Hence Hilbert space homeomorphism implies interpolation problem interval kernel L,-approximation LBA's Lemma linear subspace M₁ mapping metric projection monosplines Moreover multiplicity n)-normal nearest point neighborhood nodes normed linear space obtain one-one open set Padé approximant parameter point to f polynomial positive definite Proof rational approximation rational functions resp Rolle's theorem s₁ satisfies sequence solution spline functions strongly unique subset t₁ tangent cone tangent space Theorem theory u₁ u₂ uniform approximation unique best approximation v₁ varisolvent family x₁ y-polynomial