madeinmsia
- 15
- 0
I'm using matlab's [V,D]=eig(A,B) function to find the eigenvectors and eigenvalues given two full matrices of A and B.
I know the eigenvectors that I get are not orthonormalized, so how do I do this?
Let's say I'm solving a simple Sturm-Liouville problem like [tex]\phi''(x)}+\lambda\sigma(x)\phi(x) = 0[/tex] where [tex]\sigma(x) = 1 - x^{2}[/tex].
The general solution that I have by formulae is
[tex]\phi_{n}(x)\cong\frac{1}{\sigma^{1/4}}sin[\lambda_{n}^{1/2}\int\sigma(s)^{1/2}ds], \lambda_{n}\cong\frac{(n\pi)^{2}}{(\int\sigma(s)^{1/2}ds)^{2})}[/tex]
When I compare the graph of the eigenfunction from my formula to the numerical eigenfunction I got, they are quite similar except it looks like it is missing some weighting function.
I know the eigenvectors that I get are not orthonormalized, so how do I do this?
Let's say I'm solving a simple Sturm-Liouville problem like [tex]\phi''(x)}+\lambda\sigma(x)\phi(x) = 0[/tex] where [tex]\sigma(x) = 1 - x^{2}[/tex].
The general solution that I have by formulae is
[tex]\phi_{n}(x)\cong\frac{1}{\sigma^{1/4}}sin[\lambda_{n}^{1/2}\int\sigma(s)^{1/2}ds], \lambda_{n}\cong\frac{(n\pi)^{2}}{(\int\sigma(s)^{1/2}ds)^{2})}[/tex]
When I compare the graph of the eigenfunction from my formula to the numerical eigenfunction I got, they are quite similar except it looks like it is missing some weighting function.