Analysis

Learn Approximation Theory

What 'best approximation' means and why the norm is part of the question, Bernstein polynomials and Korovkin's theorem, the Runge phenomenon and the Lebesgue constant, equioscillation and the Remez algorithm, Jackson and Bernstein inequalities, and the constructive side from Hermite and Bezier through Pade, acceleration and spectral accuracy.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

30 lessons in Approximation Theory

What 'best' meansBernstein polynomialsKorovkin's theoremChebyshev polynomials and minimal sup normThe Lebesgue constantThe equioscillation theoremThe Remez exchange algorithmJackson's theoremBernstein's inequalityHermite interpolationBezier curves and de CasteljauPade approximantsAitken and Shanks accelerationClenshaw-Curtis quadratureNonlinear and greedy approximationKolmogorov n-widthsBarycentric interpolationSpectral accuracyChebyshev systems and the Haar conditionB-splinesShape-preserving interpolationRadial basis function interpolationRational approximationProny's methodRootfinding from a Chebyshev seriesOscillatory quadratureThe Müntz–Szász theoremThe universal approximation theoremApproximation in high dimensionsThe Kolmogorov superposition theorem
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Approximation Theory exactly where it's useful.

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