Advanced Numerical Methods for Computational and Data

Theory and practice of a selection of advanced numerical methods for computational and data sciences. Algorithms for eigenvalues and singular value decomposition. Multigrid methods for linear and nonlinear systems. Sparse optimization and compressed sensing. Low-rank tensor and matrix decomposition. Nonlinear convergence acceleration. Randomized numerical linear algebra. Adjoint methods and automatic differentiation for neural networks and optimal control. Stochastic gradient descent and variants. Efficient computer implementation of the algorithms and applications with real-world data. Students should have completed an introductory course on numerical methods.