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 methods for solving the linear algebraic systems.
Parallel QR Decomposition of a Rectangular Matrix.
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.
Partitioned Matrices and Seidel Convergence.
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...
Pivoting algorithm in class of ABS methods
Summary: The paper deals with a pivoting modification of the algorithm in the class of ABS methods. Numerical experiments compare this pivoting modification with the fundamental version. A hybrid algorithm for the solution of the linear system with the Hankel matrix is introduced.
Pivoting Techniques for Symmetrie Gaussian Elimination.
Produits rapides matrice-vecteur en bases d'ondelettes : application à la résolution numérique d'équations aux dérivés partielles