The aim of this project is to compare and analyze the behavior of the different numerical methods used for solving system of linear equations: Gauss Elimination. Gauss Jordan. LU Decomposition. Gauss ...

For more detailed explanations and formulas of each method, refer to the course materials or external resources on numerical methods.

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding ...

The course provides a thorough introduction to design, analysis (both theoretical and empirical), and programming of popular methods (finite difference and variational methods like finite element) for ...

In this paper a new ODE numerical integration method was successfully applied to solving nonlinear equations. The method is of same simplicity as fixed point iteration, but the efficiency has been ...