Fast Selected Inversion of Sparse Symmetric Matrix and Marginal Variance Calculation

Abstract: In spatial statistics, a substantial portion of computation time often goes toward matrix inversion, particularly when working with large precision matrices that are both sparse and symmetric. In many practical scenarios, however, only a small subset of the inverse's entries is required, making a full inversion computationally expensive. This thesis reviews a selected inversion algorithm that leverages the $LDL^T$ factorization and exploits the structure of the elimination tree to compute only the needed elements of the inverse. By doing so, it significantly reduces both computational effort and memory usage.

Advisor: Debashis Mondal