Updating BIF preconditioners

Professor Jose Mas

Instituto de Matemática Multidisciplinar, Universitat Politècnica de València

August 6th (Tuesday) 11:00-12:00am
National Institute of Informatics, 12th floor, Lecture room 1 (Room 1212)

Let $Ax=b$ be a large and sparse system of linear equations where $A$ is a general nonsingular matrix. An approximate
solution is frequently obtained by applying preconditioned iterations.
Consider the matrix $B=A+PQ^T$ where $P, Q \in \mathbb{R}^{n \times k}$ with $k <<n$ are full rank matrices.
Some techniques to update a previously computed preconditioner for $A$, such that the update can be used to solve
the updated linear system $Bx=b$ by preconditioned iterations will be analyzed,
in particular if the original preconditioner is computed using the BIF preconditioner.
Conditions on the matrices $P$ and $Q$ that guarantee the
invertibility of the matrix $B$ will be presented as well as the results of some numerical experiments with different types of problems.