Open Science Research Excellence

Peiyong Zhu

Publications

4

Publications

4
13163
Structure of Covering-based Rough Sets
Abstract:

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

Keywords:
Covering, poset, down-set, lattice, topological space, topological base.
3
15182
Strongly Screenableness and its Tychonoff Products
Abstract:

In this paper, we prove that if X is regular strongly screenable DC-like (C-scattered), then X ×Y is strongly screenable for every strongly screenable space Y . We also show that the product i∈ω Yi is strongly screenable if every Yi is a regular strongly screenable DC-like space. Finally, we present that the strongly screenableness are poorly behaved with its Tychonoff products.

Keywords:
Topological game, strongly screenable, scattered, Cscattered.
2
17059
Dense Chaos in Coupled Map Lattices
Abstract:

This paper is mainly concerned with a kind of coupled map lattices (CMLs). New definitions of dense δ-chaos and dense chaos (which is a special case of dense δ-chaos with δ = 0) in discrete spatiotemporal systems are given and sufficient conditions for these systems to be densely chaotic or densely δ-chaotic are derived.

Keywords:
Discrete spatiotemporal systems, coupled map lattices, dense δ-chaos, Li-Yorke pairs.
1
10000044
Global GMRES with Deflated Restarting for Families of Shifted Linear Systems
Abstract:

Many problems in science and engineering field require the solution of shifted linear systems with multiple right hand sides and multiple shifts. To solve such systems efficiently, the implicitly restarted global GMRES algorithm is extended in this paper. However, the shift invariant property could no longer hold over the augmented global Krylov subspace due to adding the harmonic Ritz matrices. To remedy this situation, we enforce the collinearity condition on the shifted system and propose shift implicitly restarted global GMRES. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solution for the shifted systems using only as many matrix vector multiplications as the solution of the seed system requires. In addition, some numerical experiments also confirm the effectiveness of our method.

Keywords:
Shifted linear systems, global Krylov subspace, GLGMRESIR, GLGMRESIRsh, harmonic Ritz matrix, harmonic Ritz vector.