New answers tagged eigenvalues
0
I believe it can be done with a semidefinite program by adding a multiplicative slack variable. Basically,
$$
\begin{array}{rcl}
\min\limits_{A \in \mathbb{R}^{n \times n}, P\in \mathbb{R}^{n\times n}} &&f(A)\\
\text{st} && b I \preceq PA + A^TP \preceq a I\\
&& P \succ 0
\end{array}
$$
Essentially, this is the Lyapunov stability ...
3
Test your code. "I don't know if my linear algebra routines work or not" is a problem you can solve easily. It is easy to check if you have computed the correct eigenvalues or not; just check that $VDV^{-1}=H$, or if you don't fancy the inversion $HV=VD$. If you are not sure that your individual pieces work, you are walking in the dark.
Possibly a hot take: ...
1
Your whole code is not understandable to me. Try this alternative components:
int grid(int i, double a, double h)
{
return a+i*h;
}
int index(int i, int j, int N)
{
return i*N+j;
}
//potential function. returns the integral over the grid square indexed by i
double V(int i, double x0, double hx, int j, double y0, double hy)
{
double xi=grid(i,...
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