I am struggling to solve a sequence of linear systems of the form
$$(x_i I + B ) y_i = b, \quad i = 1,2,\dotsc,$$
where $I$ is identity, $x_i$ is a real number and $B$ is sparse. Both the matrix $B$ and the right-hand side $b$ are independent of $x_i$. Both $B$ and $b$ are complex.
Iterative methods are inapplicable here because
$$||B^{-1}|| \,\,\,\, \text{sup}_i \,\,\, |x_{i+1} - x_i| \gg 1. $$
Can I exploit the fact that all matrices have the same sparsity pattern?