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This course focuses on the mathematical foundations of approximating high-dimensional functions from limited information, such as a small number of samples. The learning outcomes include understanding multilevel weighted least squares polynomial approximation, overcoming the curse of dimensionality, and applying modern approaches to function reconstruction. The course teaches skills such as polynomial least squares approximation, sampling from optimal density, and multilevel convergence analysis. The teaching method involves workshops featuring talks by eminent researchers in multivariate approximation theory and related areas. The intended audience for this course includes individuals interested in multivariate approximation, high-dimensional integration, and non-parametric regression.
