MATH-351: Advanced numerical analysis II

Lectures in this course (51)

Covers the concept of equivalent formulation in constrained optimization and explores the tangent cone.

Explores numerical methods for solving the wave equation, discussing stability conditions and convergence rates.

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Covers line search, Newton's method, BFGS, and conjugate gradient in nonlinear optimization.

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Explores the heat equation solutions using Fourier series and energy conservation.

Explores optimal control and KKT conditions for non-linear optimization with constraints.

Covers optimization methods, focusing on gradient methods and line search techniques.

Covers the optimization with constraints and the KKT theorem.

Covers implicit schemes in numerical analysis for solving partial differential equations.

Covers the Newton method and its convergence properties near the optimal point.

Covers the convergence and conditions for optimal control.

Covers the parabolic heat equation in two dimensions and its numerical solution methods.

Discusses the explicit Runge Kulta method for function approximation and error analysis.

Covers ODE RK schemes, including explicit RK stages and accuracy computation.

Covers optimization with constraints using KKT conditions and matrix invertibility in numerical analysis.

Discusses boundary value problems in 1D and the mathematical principles involved.

Covers high order methods for space discretisation in linear differential systems.

Explores optimal control in unconstrained and constrained problems, emphasizing the importance of sparsity.

Covers the application of optimal control in parameter identification and the trade-off between the model and measurements.

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