linear_algebra

For Homework 5

Solver for Tridiagonal

The function lu_tridiagonal and solve_tridiag were used. the test_arrays were used to get arrays A3-A10 which were decomposed using the decompose script to get the the matrix into the format for the other 2 problems. The norm of the error was calculated by norm(solverans-backslashans)

size(A)	Norm error
3	1.551583845779546e-16
4	NaN
5	1.904445134749238e-15
6	6.194784729765104e-16
7	4.833501208402912e-16
8	NaN
9	3.678329060193967e-14
10	1.951962655680467e-14

#Spring Mass System Vibrational Mode Equations:

(30-w^2)X1 - 20X2 = 0
-10X1 + (20-w^2)X2 -10X3 = 0
5X2 + (7.5-w^2)X3 = 0

Matrix used for Eigenvalues
30	-20	0
-10	20	-10
0	-5	7.5

eigenvalues were found using eig function in matlab

Eigenvalues + Natural Frequencies

lambda	omega
40.521977310645262	6.365687497092931
14.409008287895661	3.795919952777674
2.569014401459066	1.602814524971329

#Curvature of slender column

# of segments	smallest	largest	# of eigenvalues
5	0.382	3.618	4
6	0.385	5.374	5
10	0.39	15.6	9

as deltaX increases the eigenvalues continue to increase

mmg13001/linear_algebra

About

Resources

Stars

Watchers

Forks

Releases

Languages