I have a tridiagonal antiHermitian matrix with nonzero elements along the diagonal, upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a given vector. Currently, I am using scipy.sparse.linalg.expm_multiply function in Python to check the action of a million by million dimensional matrix on a million dimensional vector:scipy.sparse.linalg.expm_multiply(Hami, psi, start=0, stop=t_end-dt, num=int(t_end/dt), endpoint=True, traceA=0). This gives me the required state at various times $(e^{-i∗Hami∗t}|psi⟩)$ for $t=\{0,dt,...,t_{end}-dt\}$.

This takes multiple days to get the answer. The end goal is to do this computation for 1000s of cases. I was wondering if there is any way to accelerate such computation?

I have a tridiagonal antiHermitian matrix ($-i*Hami*t$) with nonzero elements only along the upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a given vector. Currently, I am using scipy.sparse.linalg.expm_multiply function in Python to check the action of a million by million dimensional matrix on a million dimensional vector:scipy.sparse.linalg.expm_multiply(Hami, psi, start=0, stop=t_end-dt, num=int(t_end/dt), endpoint=True, traceA=0). This gives me the required state at various times $(e^{-i∗Hami∗t}|psi⟩)$ for $t=\{0,dt,...,t_{end}-dt\}$.

This takes multiple days to get the answer. The end goal is to do this computation for 1000s of cases. I was wondering if there is any way to accelerate such computation?

I have a tridiagonal antiHermitian matrix with nonzero elements along the diagonal, upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a given vector. Currently, I am using scipy.sparse.linalg.expm_multiply function in Python to check the action of a million by million dimensional matrix on a million dimensional vector, and it seems to take multiple days to get the answer. The end goal is to do this computation for 1000s of cases. I was wondering if there is any way to accelerate such computation?

I have a tridiagonal antiHermitian matrix with nonzero elements along the diagonal, upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a given vector. Currently, I am using scipy.sparse.linalg.expm_multiply function in Python to check the action of a million by million dimensional matrix on a million dimensional vector:scipy.sparse.linalg.expm_multiply(Hami, psi, start=0, stop=t_end-dt, num=int(t_end/dt), endpoint=True, traceA=0). This gives me the required state at various times $(e^{-i∗Hami∗t}|psi⟩)$ for $t=\{0,dt,...,t_{end}-dt\}$.

This takes multiple days to get the answer. The end goal is to do this computation for 1000s of cases. I was wondering if there is any way to accelerate such computation?