Aim of the applet
Solve systems of equations by the gradient-based methods.
Implemented methods: Steepest descent, Gradiente and Conjugate Gradient.
Input data
- Coefficient matrix, A
- The right side vector, b
- Maximum number of steps.
- Tolerance.
- Initial approximation of the solution.
- The step of the Gradient method, the parmeter "α".
- Preconditioner P. It applies to the methods of gradient and conjugate gradient.
The Calculate button will make the resolution of the system by the methods of Steepest descent, Gradiente and Conjugate Gradient.
The user may specify the order of the matrix, as well as create a random matrix A
and a random right side vector b by clicking in "Random Matrix" button.
In the Options menu, can choose the size of cells.
Output data
The applet will show, for each method, the following information:
- Intermediate result table and relative errors calculated with norm 2.
- Solution obtained.
- Graphical representation of error obtained for each method.
If any of the data has been entered wrong in the input matrix,
this will be highlighted with a red border.
First steps
- Write the ecuations system:
3x - y + z = 1
-x + 6y + 2z = 0
x + 2y + 7z = 4
Try with different errors and different number of iterations.
Note that method converges faster to the solution.
Modify the parameters α and P, and observe how the convergence changes. What value of α improves the convergence?
