We consider the following linear system AX = b, where A ∈ R n×n , and b ∈ R m and X ∈ R n is unknown. The iterative matrix of the classical AOR method is L r,w = (I − rL) −1 [(I − w)I + (w − r)L + wU], where w and r are real parameters with w = 0, I is the identity matrix, L and U are strictly lower and upper triangular matrices obtained from A, respectively. The improvement in AOR method for solving this system has been carried out by Hadjimos [1], Recently, Yao-Tang et al. [2], improved AOR method which has been developed by [1]. In this work, we construct a preconditioner to improve the Accelerated Over-relaxation (AOR) iterative method for solution of linear systems. We reduce the spectral radius of iterative matrix by multiplication of Preconditioner matrix p * in to the system p * Ax = p * b. By assuming p * A = D * − L * − U * and applying the AOR method we obtained the corresponding Preconditioned AOR iterative method whose iterative matrix is: L * r,w = (D * − rL *) −1 [(1 − w)D * + (w − r)L * + wU * ]. We improve the convergence rate of the presented iterative method and generalized the results. The convergence analysis of AOR method has been improved. Main while our method can be used to more class of the linear systems.
This article introduces a new IText technology called Classroom Salon. The goal of Classroom Salon is to bring some of the benefits of social media—the expression of personal identity and community—to writing classrooms. It provides Facebook-like features to writing classes, where students can form social networks as annotators within the drafts of their peers. The authors discuss how the technology seeks to capture qualities of historical salons, which also built communities around texts. They also discuss the central features of the Classroom Salon system, how the system changes the dynamics of the writing classroom, current efforts to evaluate it, and future directions.
Use of computers in education is now ubiquitous. Students have access to course media through a variety of devices including PCs, tablets, and smart phones. The data generated by online learning platforms have the potential to change the way we teach and learn. In this brief survey paper, we explore the role of analytics in teaching and learning. In particular, how learning analytics can lead to educational process innovation. We will explore history, current state, tools, privacy issues, case studies, and future potential for analyticsbased education.
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