- #1
eckiller
- 44
- 0
I have the tridiagonal matrix (which comes from the backward Euler scheme)
A =
[ 1+2M - M 0 ... ]
[ -M 1+2M 0 ... ]
[ ... ]
[ -M 1+2M ]
I am given that the eigenvectors are v_k = [ sin(pi*k*x_j ] for j = 1:J-1 and k = 1:J-1
I am to find the eigenvalues L_k.
I tried just writing A * v_k = L_k * v_k
Then doing the multiplication on the left hand side I can get a relationship from one equation:
-M*sin(sin(pi*k*x_j-1) + (1+2M)sin(pi*k*x_j) -M*sin(pi*k*x_j+1) = L_k * sin(pi*k*x_j)
I get stuck here. Is this the right approach? Is there someway to solve for L_k?
Also: I am to show the v_k are orthogonal. Would I use dot product or the integral inner product to show this?
Thanks for any help.
A =
[ 1+2M - M 0 ... ]
[ -M 1+2M 0 ... ]
[ ... ]
[ -M 1+2M ]
I am given that the eigenvectors are v_k = [ sin(pi*k*x_j ] for j = 1:J-1 and k = 1:J-1
I am to find the eigenvalues L_k.
I tried just writing A * v_k = L_k * v_k
Then doing the multiplication on the left hand side I can get a relationship from one equation:
-M*sin(sin(pi*k*x_j-1) + (1+2M)sin(pi*k*x_j) -M*sin(pi*k*x_j+1) = L_k * sin(pi*k*x_j)
I get stuck here. Is this the right approach? Is there someway to solve for L_k?
Also: I am to show the v_k are orthogonal. Would I use dot product or the integral inner product to show this?
Thanks for any help.