This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by full algebraic (BAMG) setup algorithm that includes an AMG eigensolver, it is illustrated how can be simplified case a discretized equation (PDE), thereby developing geometric (BMG) approach. We illustrate numerically efficacy BMG metho...

• We did a general review of the manuscript checking grammar and typos suggested by reviewers. have added three SAGE codes Reviewer #1. #1 to include statistics comparing with other computer algebra system. However, we consider that this goes beyond aim our since objective is not focus on performance algorithms, rather are introducing methodology compute algebraic combinatorial structure outerp...

We propose a new predictor-corrector (PC) interior-point algorithm (IPA) for solving linear complementarity problem (LCP) with P*(?)-matrices. The introduced IPA uses type of algebraic equivalent transformation (AET) on the centering equations system defining central path. technique was by Darvay and Takács (2018) optimization. search direction discussed in this paper can be derived from positi...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic perspective and compared to ea...

For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduc...

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion contractive mappings over formal contexts is proposed, which can viewed as a generalization interior operators on sets into framework FCA. Then, by considering subset-selections consistent with mappings, notions attribute continuous ...