Approximation theory study group

The group currently consists of 6 people from different schools/departments within the College of Engineering. The goal is to learn the basic theory while implementing some practical approaches to the approximation of scattered data in 1, 2, 3, and n dimensions. Currently the main book is the "Scattered Data Approximation". We may refer to other books on approximation theory, numerical analysis, functional analysis, distribution theory and Fourier transforms, scattered data approximation, curves and surfaces, computer aided geometric design.

Resources

Snapshots and notes

Code implementations will be collected in the Sage worksheets.

Example topics to be covered

Polynomial/Hermite/Spline/Trigonometric interpolation; Taylor/Lagrange/Bernstein/Chebyshev polynomials; function spaces, existence, uniqueness and convergence; piecewise polynomials and B-splines; Bézier curves and surfaces; multivariate/tensor-product/radial-basis-function approximation; least squares and moving least squares approximation; point-set surface; approximation by convolution; Quasi-intepolation. Kriging.

RBF topics: positive definite and conditionally positive definite functions, unisolvency and polynomila resporiction, etc.

Preliminary exploration

Books

  • Holger Wendland's "Scattered Data Approximation"
  • A Course in Approximation Theory by Elliott Ward Cheney and William Allan Light
  • Farin, Curves and Surfaces for CAGD: A Practical Guide
  • All other books we can find for reference

Schedule

Every Monday 3pm in 448 Erskine


Inquiries: Igor Rychkov

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