Optimal equivalent preconditioners

The numerical solution of linear elliptic partial differential equations often involves finite element discretization, where the discretized system is usually solved by some conjugate gradient method. The crucial point in the solution of the obtained ...

Let Ax = b be a large and sparse system of linear equations where A is a nonsingular matrix. An approximate solution is frequently obtained by applying preconditioned iterations. Consider the matrix B = A + PQT where P,Qźźn k$P, Q \in \mathbb {R}^{n \...

\noindent We propose and examine block-diagonal preconditioners and variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. That is, we consider the nonsymmetric, nonsingular case where the (2,2) block is small in ...