Subspace correction methods for nonsymmetric parabolic problems

Subspace Correction Methods for Eigenvalue Problems 313

Iterative Methods by Spd and Small Subspace Solvers for Nonsymmetric or Indefinite Problems

This paper is devoted to a class of iterative methods for solving nonsymmetric or indeenite problems that are dominated by some SPD (symmetric positive deenite) problems. The algorithm is based on a direct solver for the original equation restricted on a small subspace and a given iterative method for the SPD equation. It is shown that any convergent iterative method for the SPD problem will gi...

Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration

The BiCG and QMR methods are well-known Krylov subspace iterative methods for the solution of linear systems of equations with a large nonsymmetric, nonsingular matrix. However, little is known of the performance of these methods when they are applied to the computation of approximate solutions of linear systems of equations with a matrix of ill-determined rank. Such linear systems are known as...

On Squaring Krylov Subspace Iterative Methods for Nonsymmetric Linear Systems

The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gra­ dients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orth...

Substructuring Methods for Parabolic Problems

Domain decomposition methods without overlapping for the approximation of parabolic problems are considered. Two kinds of methods are discussed. In the rst method systems of algebraic equations resulting from the approximation on each time level are solved iteratively with a Neumann-Dirichlet preconditioner. The second method is direct and similar to certain iterative methods with a Neumann-Neu...