Obtaining bounds on the two norm of a matrix from the splitting lemma.
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian.
On a non-stagnation condition for GMRES and application to saddle point matrices.
On algebraic multilevel methods for non-symmetric systems - convergence results.
On fast factorization pivoting methods for sparse symmetric indefinite systems.
On multiresolution methods in numerical analysis.
On preconditioning Schur complement and Schur complement preconditioning.
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On selection of interface weights in domain decomposition methods
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.
On the choice of iteration parameters in the Stone incomplete factorization
The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...
On the fast reduction of symmetric rationally generated Toeplitz matrices to tridiagonal form.