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+PQT where P,QRn×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.

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