04_linear_algebra
Homework 4
#PROBLEM 2#
#PART A#
H = (hilb(4));
N1 = norm(H,1)
N2 = norm(H,2)
Nf = norm(H, 'fro')
Ni = norm(H, inf)
N1 = 2.0833
N2 = 1.5002
Nf = 1.5097
Ni = 2.0833
H = (hilb(5));
N1 = norm(H,1)
N2 = norm(H,2)
Nf = norm(H, 'fro')
Ni = norm(H, inf)
N1 = 2.2833
N2 = 1.5671
Nf = 1.5809
Ni = 2.2833
#PART B#
H = inv((hilb(4)));
N1 = norm(H,1)
N2 = norm(H,2)
Nf = norm(H, 'fro')
Ni = norm(H, inf)
N1 = 1.3620e+04
N2 = 1.0341e+04
Nf = 1.0342e+04
Ni = 1.3620e+04
H = inv((hilb(5)));
N1 = norm(H,1)
N2 = norm(H,2)
Nf = norm(H, 'fro')
Ni = norm(H, inf)
N1 = 4.1328e+05
N2 = 3.0414e+05
Nf = 3.0416e+05
Ni = 4.1328e+05
#Part C#
H = (hilb(4));
condN2 = (cond(H))
condN1 = (cond(H, 1))
condNf = (cond(H, 'fro'))
condNi = (cond(H, inf))
condN2 = 1.5514e+04
condN1 = 2.8375e+04
condNf = 1.5614e+04
condNi = 2.8375e+04
H = (hilb(5));
condN2 = (cond(H))
condN1 = (cond(H, 1))
condNf = (cond(H, 'fro'))
condNi = (cond(H, inf))
condN2 = 4.7661e+05
condN1 = 9.4366e+05
condNf = 4.8085e+05
condNi = 9.4366e+05
#PART 3-4#
REFER TO .m FILES IN REPOSITORY
#PROBLEM 5#
Stiffness Matrix A + Error
k = 1000;
k1 = k;
k2 = k;
k3 = k;
k4 = k;
K = [k1+k2,-k2,0,0;-k2,k2+k3,-k3,0;0,-k3,k3+k4,-k4;0,0,-k4,k4];
x = cond(K)
e = esp*x
CONDITION = x = 29.2841
ERROR = e = 6.5024e-15
Stiffness Matrix B + Error
k = 1000;
k1 = k;
k2 = 1000*10^12;
k3 = k;
k4 = k;
K = [k1+k2,-k2,0,0;-k2,k2+k3,-k3,0;0,-k3,k3+k4,-k4;0,0,-k4,k4];
x = cond(K)
e = esp*x
CONDITION = x = 4.2361e12
ERROR = e = 9.4060e-04
Stiffness Matrix C + Error
k = 1000;
k1 = k;
k2 = 1000*10^-12;
k3 = k;
k4 = k;
K = [k1+k2,-k2,0,0;-k2,k2+k3,-k3,0;0,-k3,k3+k4,-k4;0,0,-k4,k4];
x = cond(K)
e = esp*x
CONDITION = x = 4.1493e17
ERROR = e = 92.1326
#PROBLEM 6#
PART A
k = 1000;
k1 = k;
k2 = k;
k3 = k;
k4 = k;
e = [-k2,-k3,-k4];
f = [k1+k2,k2+k3,k3+k4,k4];
[d,u] = chol_tridiag(e,f);
b = [1;1;1;1];
[x] = solve_tridiag(u,d,b)
X = DISPLACEMENTS(meters): x1 = 0.0025, x2 = 0.0050, x3 = 0.0075, x4 = 0.0100
PART B
k = 1000;
k1 = k;
k2 = 1000*10^12;
k3 = k;
k4 = k;
e = [-k2,-k3,-k4];
f = [k1+k2,k2+k3,k3+k4,k4];
[d,u] = chol_tridiag(e,f);
b = [1;1;1;1];
[x] = solve_tridiag(u,d,b)
X = DISPLACEMENTS(meters): x1 = 0.0023, x2 = 0.0023, x3 = 0.0047, x4 = 0.0070
PART C
k = 1000;
k1 = k;
k2 = 1000*10^-12;
k3 = k;
k4 = k;
e = [-k2,-k3,-k4];
f = [k1+k2,k2+k3,k3+k4,k4];
[d,u] = chol_tridiag(e,f);
b = [1;1;1;1];
[x] = solve_tridiag(u,d,b)
X = DISPLACEMENTS(meters x 10^9): x1 = 0.0030, x2 = 3.0087, x3 = 3.0057, x4 = 2.9997
#PROBLEM 7#
Function stored as .m file in repository
Answer is most likely wrong
[v,w] = mass_spring_vibrate(10,20,20,10)
v =
-0.8892 -0.7282 0.5219
0.4561 -0.6222 0.6699
-0.0348 0.2873 0.5280
w =
6.3450 0 0 < -- Natural Freq m1
0 3.5935 0 < -- Natural Freq m2
0 0 2.0804 < -- Natural Freq m3
#PROBLEM 8#
| # of segments | largest load (N) | smallest load (N) | # of eigenvalues |
|---|---|---|---|
| 5 | 10999 | 1161 | 4 |
| 6 | 16337 | 1173 | 5 |
| 10 | 47450 | 1190 | 9 |