Linear System

Matrix solvers.

Note

Although the functions implemented here behave similarly as the ones in LAPACK, there are two major differences:

• No pivoting

  Although functions in LAPACK include pivoting operations to stabilize the system, we do not do that for simplicity, assuming all systems are well-conditioned.

• Treatment of the singularity

  When a singularity is detected, functions in LAPACK report it and terminate. Although this often makes sense, in this project, such exception should be treated gracefully, as singular systems are highly expected due to the imposed Neumann or the periodic boundary conditions.

• Gauss-Jordan method
• Gaussian elimination
• Thomas Algorithm