update

helpfile.m

@@ -1 +1,19 @@
-help file
+
+
+
+  test_arrays 
+ fprintf('size of Matrix               error \n');
+  for i=3:10;
+   [ud,uo,lo]=lu_tridiag(e(1:i-1),f(1:i),g(1:i-1));
+   b=ones(i,1);
+   x=solve_tridiag(ud,uo,lo,b);
+   A=eval(['A',int2str(i)]);
+   y=A\b;
+
+   z=norm(x-y);
+
+  fprintf('       %d       ',i);
+  fprintf('   %6.28f \n' ,z);
+  end 
+
+

lu_tridiag.m

@@ -1,6 +1,6 @@
-function [ud,uo,lo]=lu_tridiag(e,f,g);
+function [ud,uo,lo]=lu_tridiag(g,f,e);
   % lu_tridiag calculates the components for LU-decomposition of a tridiagonal matrix
-  % given its off-diagonal vectors, e (a) and g (b)
+  % given its off-diagonal vectors, e (n=0) and g (1=0)
   % and diagonal vector f (d)
   % the output is 
   % the diagonal of the Upper matrix, ud (dd)
@@ -11,14 +11,19 @@ function [ud,uo,lo]=lu_tridiag(e,f,g);
 ud=zeros(m,n);
 uo=zeros(m,n);
 lo=zeros(m,n);
+
+
 ud(1)=f(1);
 lo(1)=0;
-uo=e;
 
+for s=1:(m-1)
+uo(s)=e(s);
+end 
+uo(m)=0; 
 
-for i=2:n
-    lo(i)=g(i)/(ud(i-1));
-    ud(i)=f(i)-(lo(i)*e(i-1));
+for i=2:m
+    lo(i,1)=g(i-1,1)/(ud(i-1,1));
+    ud(i,1)=f(i,1)-(lo(i,1)*e(i-1,1));
 end 
 
 

question6.m

@@ -0,0 +1,22 @@
+clc;
+clear;
+
+BeamLength=5;
+NumSegments=10;
+deltax=BeamLength/NumSegments;
+
+n=NumSegments-1;
+A=zeros(n,n);
+
+for i=1:n
+    A(i,i)=2;
+end
+
+for i= 1:n-1
+    A(i,i+1)=-1;
+    A(1+i,i)=-1;
+end
+A(n,n)=-3
+
+eig(A)
+

solve_tridiag.m

@@ -14,18 +14,22 @@ z(1)=b(1);
 x=zeros(s,n);
 
 
+
 %solve Lz=b using forward subsitution
-for i= 2:n
-    z(i)=b(i)-(lo(i)*z(i-1));
+for i= 2:s
+  z(i)=b(i)-(lo(i)*z(i-1));
+
 end 
 
 %solve Ux=z using backward substitution
-x(n)=z(n)/ud(n);
+x(s)=z(s)/ud(s);
 
-for k= (n-1):-1:1 
+for k= (s-1):-1:1 
 
     x(k)=(z(k)-uo(k)*x(k+1))/ud(k);
 end
+
+
 end
 
 

springmass.m

@@ -0,0 +1,12 @@
+k1=10;
+k2=20;
+k3=20;
+k4=10;
+m1=1;
+m2=2;
+m3=4;
+km=[(1/m1)*(k2+k1),-(k2/m1),0;-(k2/m2),(1/m2)*(k2+k3),-(k3/m2);0,-(k3/m3),(1/m3)*(k3+k4)];
+
+eigenvalues=eig(km)
+
+frequencies=sqrt(eigenvalues)

test_arrays.m

@@ -1,8 +1,8 @@
-rand("seed",1);
+
 
 for i = 3:10
   e=sort(randi(6,[i-1,1]));
   f=sort(randi(10,[i,1]));
   g=sort(randi(9,[i-1,1]));
   eval(['A',int2str(i),'=diag(f)+diag(e,-1)+diag(g,1);']);
-end
+end