Multilevel Weighted Least Squares Polynomial Approximation – Sören Wolfers, KAUST
Alan Turing Institute via YouTube
Overview
Syllabus
Intro
Polynomial least squares approximation
Accuracy - Summary
Accuracy - References
Sampling from optimal density
Single level approach to inexact evaluations Ides Apply least squares approximation to freed to Problem: Good approximation requires both a large subspace
Multilevel approach to inexact evaluations
Multilevel convergence analysis
Numerical example Stationary diffusion equation with random coefficient field
Setup
Curse of dimensionality
Smolyak decomposition
Decay of mixed differences
Adaptive algorithm
Special case multilevel polynomial approximation
Taught by
Alan Turing Institute