Domains of Divergence of the USSOR Method Applied on p-Cyclic Matrices.
Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media.
Eigenvalues of certain sparse matrices
Error analysis and computational aspects of SR factorization via optimal symplectic householder transformations.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Finding nonoverlapping substructures of a sparse matrix.
Forward Error Analysis of Gaussian Elimination. Part II: Stability Theorems.
Gradient descent and fast artificial time integration
The integration to steady state of many initial value ODEs and PDEs using the forward Euler method can alternatively be considered as gradient descent for an associated minimization problem. Greedy algorithms such as steepest descent for determining the step size are as slow to reach steady state as is forward Euler integration with the best uniform step size. But other, much faster methods using bolder step size selection exist. Various alternatives are investigated from both theoretical and practical...
Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem.
Homogeneous Jacobi-Davidson.
Iterative algorithms with seminorm-induced oblique projections.
Joint domain-decomposition -LU preconditioners for saddle point problems.
Locality of reference in sparse Cholesky factorization methods.
Low rank Tucker-type tensor approximation to classical potentials
This paper investigates best rank-(r 1,..., r d) Tucker tensor approximation of higher-order tensors arising from the discretization of linear operators and functions in ℝd. Super-convergence of the best rank-(r 1,..., r d) Tucker-type decomposition with respect to the relative Frobenius norm is proven. Dimensionality reduction by the two-level Tucker-to-canonical approximation is discussed. Tensor-product representation of basic multi-linear algebra operations is considered, including inner, outer...
Minimization properties and short recurrences for Krylov subspace methods.
Numerical experiments with algebraic multilevel preconditioners.
Numerical stability of the cyclic Richardson iteration.
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.