I have a large sparse $n \times n$ matrix $A$, which generally is not diagonally dominant. This answer provides an estimate assuming diagonal dominance, but it looks to be inappropriate for the non-diagonally dominant case (the numerator here would be negative).
I am aware of Krylov solvers that estimate eigenvalues en route to a solution; is there a more general way of directly estimating the spectral radius of a matrix with less cost than a full eigenvalue computation?
Some properties of $A$, if it matters:
- $A$ is invertible
- $A$ is usually symmetric
- $A$ has non-zero diagonal
- Coefficients of $A$ may be positive or negative