Speaker
Description
In this talk we consider the problem of finding effective preconditioners for linear systems of the form $Hx = y$ where
$$
H = A^T D A + \lambda^2 L^T L
$$
where $A$ and $L$ are structured matrices (e.g., Toeplitz), $D$ is a diagonal matrix, and $\lambda$ is a scalar.
These linear systems can arise when iteratively computing approximations to nonlinear inverse problems. Typically in these applications the matrix $D$ changes at each nonlinear iteration, but $A$ and $L$ remain constant. Benzi and Ng [1] considered linear systems of this form, and proposed an effective variant of constraint preconditioning and a Hermitian/skew-Hermitian splitting (HSS) preconditioner. In this talk we consider an alternative approach based on low-rank matrix approximations.
References
[1] M. Benzi, M. K. Ng Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems SIAM J. Matrix Anal. Appl., 27 (2006), pp. 1106–1124.
