Optimally rotated vectors.
Optimally Scaled Matrices, Necessary and Sufficient Conditions.
Optimizing tensor product computations in stochastic automata networks
Optimum Stationary and Nonstationary Iterative Methods for the Solution of Singular Linear Systems.
Orthogonal polynomials and quadrature.
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....
Orthogonalization, factorization, and identification as to the theory of recursive equations in linear algebra.
-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 and superfast algorithms for Hankel systems of equations.
Parallel cyclic odd-even reduction algorithms for solving general tridiagonal periodic systems on parallel computers
Parallel fully coupled Schwarz preconditioners for saddle point problems.
Parallel Interval Multisplittings.
Parallel methods for solving partial differential equations
Parallel methods for solving the linear algebraic systems.
Parallel QR Decomposition of a Rectangular Matrix.
Parallel solution of elasticity problems using overlapping aggregations
The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between elements...
Parallel strategies for solving the FETI coarse problem in the PERMON toolbox
PERMON (Parallel, Efficient, Robust, Modular, Object-oriented, Numerical) is a newly emerging collection of software libraries, uniquely combining Quadratic Programming (QP) algorithms and Domain Decomposition Methods (DDM). Among the main applications are contact problems of mechanics. This paper gives an overview of PERMON and selected ingredients improving scalability, demonstrated by numerical experiments.
Parallel SVD computation
Parallel, synchronous and asynchronous two-stage multisplitting methods.