Crout versions of ILU factorization with pivoting for sparse symmetric matrices.
Decomposition of a Symmetric Matrix (Handbook Series Linear Algebra).
Derivation of high-order spectral methods for time-dependent PDE using modified moments.
Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems.
Displacement preconditioner for Toeplitz least squares iterations.
Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media.
Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems.
Efficient preconditioning for sequences of parametric complex symmetric linear systems.
Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.
Eigenvalue condition numbers and a formula of Burke, Lewis and Overton.
Eigenvalues of graded matrices and the condition numbers of a multiple eigenvalue.
Erratum. On the Multi-Level Splitting of Finite Element Spaces.(Numer. Math. 49, 379-412 (1986)).
Estimating the matrix p-norm.
Euclid΄s algorithm and accelerated iterative methods
Evaluating the Frechet derivative of the matrix exponential.
Evaluation of the condition number in linear systems arising in finite element approximations
This paper derives upper and lower bounds for the -condition number of the stiffness matrix resulting from the finite element approximation of a linear, abstract model problem. Sharp estimates in terms of the meshsize h are obtained. The theoretical results are applied to finite element approximations of elliptic PDE's in variational and in mixed form, and to first-order PDE's approximated using the Galerkin–Least Squares technique or by means of a non-standard Galerkin technique in L1(Ω). Numerical...
Explicit conjugate gradient method with preconditioning
An algorithm of the preconditioned conjugate gradient method in which the solution of an auxiliary system is replaced with multiplication by the matrix for suitably chosen is presented.
Fast Givens transformation for quaternion valued matrices applied to Hessenberg reductions.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Finite-difference preconditioners for superconsistent pseudospectral approximations
The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented...