-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.
Partial convergence and sign convergence of matrix powers via eigen c-ads.
Partitioned Matrices and Seidel Convergence.
Partitioning inverse Monte Carlo iterative algorithm for finding the three smallest eigenpairs of generalized eigenvalue problem.
Pentadiagonal Companion Matrices
The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find a Fiedler...
Performance of parallel QR factorization methods on the NVIDIA Grace CPU Superchip
This article studies several algorithms for QR factorization based on hierarchical Householder reflectors organized into elimination trees, which are particularly suited for tall-and-skinny matrices and allow parallelization. We examine the effect of various parameters on the performance of the tree-based algorithms. The work is accompanied with a custom implementation that utilizes a task-based runtime system (OpenMP or StarPU). The same algorithm is implemented in the PLASMA library. The performance...
Periodické distribuce a diskrétní Fourierova transformace
Perturbation analysis for eigenstructure assignment of linear multi-input systems.