Lectures related to Nonlinear Systems of Equations

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

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

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Covers Newton-Krylov-hookstep methods for finding roots of high-dimensional systems.