A bound for the Moore-Penrose pseudoinverse of a matrix
A Class of Norms of Iterative Methods for Solving Systems of Linear Equations.
A Contribution to the Theory of Condition.
A domain embedding method for Dirichlet problems in arbitrary space dimension
A FETI-DP preconditioner for mortar methods in three dimensions.
A hierarchical preconditioner for the mortar finite element method.
A Legendre spectral collocation method for the biharmonic Dirichlet problem
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a...
A multigrid algorithm for higher order finite elements on sparse grids.
A network programming approach in solving Darcy's equations by mixed finite-element methods.
A Note on Optimal Block-Scaling of Matrices.
A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.
A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems
In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal.24 (2004)...
A posteriori error estimates for linear equations.
A Symmetric Numerical Range for Matrices.
A two parameter iterative method for solving algebraic systems of domain decomposition type
An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains
Adaptive mixed hybrid and macro-hybrid finite element methods.
Additive Schwarz algorithms for parabolic convection-diffusion equations.
Additive Schwarz methods for the p-version finite element method.