Floating point arithmetic. Numerical linear algebra: Singular Value
Decomposition, QR and LU factorizations. Eigenvalues and
eigenvectors. Systems of non-linear equations: functional iteration,
Newton"s method. Numerical Differential Equations: basic integration
schemes, order of accuracy. Initial Value Problem: Euler method,
explicit-implicit methods, stability, Runge-Kutta methods, adaptive
step size. Boundary Value Problem: shooting method,
quasi-linearization. Other topics as chosen by the instructor.
Part B (Spring)
Least squares problem. Unconstrained Optimization: gradient
descent with backtracking, Newton method; constrained
optimization: primal-dual Newton, interior point methods; linear
programming. Inference and Learning Algorithms: sampling
algorithms, Monte-Carlo method, importance sampling, stochastic
optimization; regression, classification, clustering. Other topics
as chosen by the instructor.