Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to a large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connecte...

SYM-ILDL is a numerical software package that computes incomplete LDLT (or ‘ILDL’) factorizations of symmetric indefinite and skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by [Li and Saad, Crout versions of ILU factorization with pivoting for sparse symmetric matrices, Transactions on Nu...

We investigate two iterative methods for solving nonsingular linear systems P(A)x = b; () where P(A) = P p i=0 i A i denotes a matrix polynomial and A is hermitian. The key idea of the methods is to choose the approximate solutions x j from the Krylov subspaces with respect to the matrix A instead of P(A). Thus, only one matrix vector multiplication (Gemv) is necessary to extend the current Kry...

We consider a generalized Stokes equation with problem parameters 0 (size of the reaction term) and >0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess–Sarazin and Vanka-type smooth...

A method is proposed for reducing the cost of computing search directions in an interior point method for a quadratic program. The KKT system is partitioned and modified, based on the ratios of the slack variables and dual variables associated with the inequality constraints, to produce a smaller, approximate linear system. Analytical and numerical results are included that suggest the distribu...

We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an H(div) operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the ArnoldFalk-Winther multigrid algorith...

The convergence of numerical approximations to the solutions of differential equations is a key aspect of Numerical Analysis and Scientific Computing. Iterative solution methods for the systems of linear(ised) equations which often result are also underpinned by analyses of convergence. In the function space setting, it is widely appreciated that there are appropriate ways in which to assess co...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

هدف: پژوهش حاضر با هدف ساخت برنامه داربست‌سازی انگیزشی و تعیین اثربخشی آن بر جهت‌گیری‌های هدفی ارزیابی‌های شناختیوالدین انجام شد. روش: پس از طراحی آموزشی داربست سازی اساس نقشه نگاری مداخله، به منظور بررسی شبه‌آزمایشی طرح پیش‌آزمون ـ پس‌آزمون همراه پیگیری گروه گواه استفاده جامعه آماری شامل تمامی والدین ­دانش‌آموزان پایه هشتم منطقة 4 آموزش پرورش شهر تهران نمونة نیز 30 مادر دارای فرزند کلاس هفتم ب...

هدف: آینده­ نگری مجموعه ­ای از توانایی­ های شناختی است. که شامل پیش­ بینی حالت­ ممکن آینده و نیازهای خود این مهارت برای برنامه­ ریزی، غلبه بر موانع رسیدن به موفقیت افراد کمک می­کند. یکی جدیدترین ابزارهای سنجش توانایی تفکر آینده­نگر در کودکان، مقیاس کودکان (مازاچووسکای مهی، 2020) است ویژگی­ روان­سنجی آن استفاده جمعیت ایرانی مورد مطالعه قرار نگرفته روش: روش پژوهش حاضر توصیفی مقطعی بود. تعداد 200 ...