On the Multi-Level Splitting of Finite Element Squares.
On the Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements
The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.
On the Quadratic Convergence of the Special Cyclic Jacobi Method.
On the Rate of Convergence of the Preconditioned Conjugate Gradient Method.
On the set of weighted least squares solutions of systems of convex inequalities
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the Solution of Singular Linear Systems of Algebraic Equations by Semiiterative Methods.
On the subspace projected approximate matrix method
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix . It falls in the category of inner-outer iteration methods and aims to reduce the costs of matrix-vector products with within its inner iteration. This is done by choosing an approximation of , and then, based on both and , to define a sequence of matrices that increasingly better approximate...
On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.
On Transformations of Graded Matrices, with Applications to Stiff ODE's.
On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block.
Optimal Successive Overrelaxation Iterative Methods fo P-Cyclic Matrices.
Optimality Relationships for p-Cyclic SOR.
Optimizing tensor product computations in stochastic automata networks
Optimum Stationary and Nonstationary Iterative Methods for the Solution of Singular Linear Systems.
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....
-regular splitting iterative methods for non-Hermitian positive definite linear systems.
Padesát let metody sdružených gradientů aneb Zvládnou počítače soustavy milionů rovnic o milionech neznámých?
Parallel fully coupled Schwarz preconditioners for saddle point problems.