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LU-decomposition function is presented in the lu_tridiag.m file.
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The function was tested using test_arrays.m file.
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Test your function on the matrices A3, A4, ..., A10 generated with test_arrays.m Solving for b=ones(N,1); where N is the size of A. In your README.md file, compare the norm of the error between your result and the result of AN\b.
To calculate the error in matlab, I used the norm function by typing in NORM' at the end of my code.
| size of A | norm(error) |
|---|---|
| 3 | 2.3414572118 |
| 4 | 1.508931741 |
| 5 | 2.7183537012 |
| 6 | 2.995245881 |
| 7 | 2.1975878506 |
| 8 | 2.2726826 |
| 9 | 1.256568519597 |
| 10 | 0.0000000000000001092 |
- These are the lambda and omega values found through the slender_column.m file:
| lambda | Omega |
|---|---|
| 2.5690 | 1.6028 |
| 14.4090 | 3.7959 |
| 40.5220 | 6.3657 |
These are the eigenvalues that were produced through the Pole_Vaulting.m file:
| # of segments | largest | smallest | # of eigenvalues | | ------------- | ------- | -------- | ---------------- | | | 5 | 3.6163 | 0.3803 | 4 | | 6 | 3.7310 | 0.2669 | 5 | | 10 | 3.9018 | 0.0976 | 9 |