Numerical Analysis for Engineering - Assignment 3 - Successive Over-Relaxation (SOR) Method

Costa Rica Institute of Technology

CE3102: Numerical Analysis for Engineering

Computer Engineering

Semester II - 2019

Assignment 3

Questions

1. Implement a function for the iterative relaxation method in Octave or Python to solve a system of linear equations of the form $Ax = b$. The name of this function should be relajacion. Indicate which are the initial parameters and which are the output parameters.

2. Implement a function for the natural cubic spline interpolation method in Octave or Python, considering the ordered pairs $(x_0, y_0), (x_1, y_1), ..., (x_n, y_n)$. The name of this function should be trazador_cubico. Note: The implementation of this method requires solving a system of linear equations. For this, use the iterative relaxation method. Indicate which are the initial parameters and which are the output parameters.

3. Consider the following table, which represents ordered pairs of the form $(x_n, y_n)$:

   n	(x_n)	(y_n)
   0	-5	0
   1	-4.5	0.0707
   2	-4	0
   3	-3.5	-0.0909
   4	-3	0
   5	-2.5	0.1273
   6	-2	0
   7	-1.5	-0.2122
   8	-1	0
   9	-0.5	0.6366
   10	0	1.0000
   11	0.5	0.6366
   12	1	0
   13	1.5	-0.2122
   14	2	0
   15	2.5	0.1273
   16	3	0
   17	3.5	-0.0909
   18	4	0
   19	4.5	0.0707
   20	5	0

Implement a script that plots the natural cubic spline passing through the above points. The name of the file should be pregunta1.