## Nonlinear approximation theory |

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### Contents

Some Notation Definitions and Basic Facts | 1 |

Linear and Convex Chebyshev Approximation | 11 |

The Functional Analytic | 24 |

Copyright | |

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### Common terms and phrases

algorithm alternant of length approximation problem approximation to f approximatively compact arguments Assume Banach space bounded Braess canonical points characteristic numbers characterization Chebyshev approximation Chebyshev set choose compact set consider construction contains continuous converges convex set Corollary critical point defined derivatives Descartes family differentiable element Example Exercise existence set exponential sums finite follows Gaussian quadrature given global Haar condition Haar cone Haar subspace Hence Hilbert space holds homeomorphism implies inequality interpolation problem kernel LBA's Lemma linear subspace Lp-approximation mapping metric projection monosplines Moreover nearest point neighborhood non-degenerate nonlinear approximation normed linear space number of zeros obtain Obviously one-one Pade approximant parameter polynomial positive definite prove rational approximation rational functions resp Rolle's theorem satisfies Show sign changes solution spline functions strict sun strong uniqueness subinterval subset tangent cone tangent space theory unique best approximation varisolvent family vector