linear_algebra
#Homework 5 2.)
The LU decomposition is excuted by using the folling functions:lu_tridiag.m.
solve_tridiag.m is used to solve the x vector in the equation Ax = B
test_array.m forms the matrix which is then decomposed.
3.)
The table below compares the error between the created code and AN\b
| size of A | norm(error) |
|---|---|
| 3 | 2.341457211866148746537419356 |
| 4 | 1.5089317413322578254053496494 |
| 5 | 2.718353701243559239486557999 |
| 6 | 2.9952458816401601460199799476 |
| 7 | 2.1975878506014523416922656907 |
| 8 | 2.2726826857500208589613066579 |
| 9 | 1.2565685195978946175898727233 |
| 10 | 0.0000000000000001092738104726 |
The table below shows the values of lamda and omega
| lamda | omega |
|---|---|
| 40.5220 | 6.3657 |
| 14.4090 | 3.7959 |
| 2.5690 | 1.6028 |
The table below expresses the values produced in the column.
| # of segments | smallest | largest | number of eigenvalues |
|---|---|---|---|
| 5 | 0.382 | 3.618 | 4 |
| 6 | 0.385 | 5.374 | 5 |
| 10 | 0.39 | 15.6 | 9 |