The Bramble-Pasciak Conjugate Gradient method is a well known tool to solve linear systems in saddle point form. A drawback of this method in order to ensure applicability of Conjugate Gradients is the need for scaling the preconditioner which typically involves the solution of an eigenvalue problem. Here, we introduce a modified preconditioner and inner product which without scaling enable the...

Abstract. We consider saddle point problems that result from the finite element discretization of stationary and instationary Stokes equations. Three efficient iterative solvers for these problems are treated, namely the preconditioned CG method introduced by Bramble and Pasciak, the preconditioned MINRES method and a method due to Bank et al. We give a detailed overview of algorithmic aspects ...

Elliptic optimal control problems with pointwise state gradient constraints are considered. A quadratic penalty approach is employed together with a semismooth Newton iteration. Three different preconditioners are proposed and the ensuing spectral properties of the preconditioned linear Newton saddle-point systems are analyzed in dependence on the penalty parameter. A new bound for the smallest...

هدف: هدف از این پژوهش بررسی واسطه‌­ای راهبردهای سازش نایافته تنظیم شناختی هیجان در رابطه باورهای فراشناختی با اضطراب امتحان بود. روش: روش حاضر توصیفی و نوع همبستگی جامعه آماری را کلیه دانش‌­آموزان پسر دوره دوم متوسطه شهر تهران سال تحصیلی 1401-1400 تشکیل دادند که تعداد 456 نفر به نمونه‏‌گیری دسترس انتخاب شرکت کردند. ابزارها شامل سیاهه ابوالقاسمی همکاران (1375)، پرسشنامه باکو دیگران (2009)، فرم ک...

Solving a large, sparse, symmetric linear system Ax = b iteratively must use appropriate methods. The conjugate gradient (CG) method can break down if A is indefinite while algorithms such as SYMMLQ and MINRES, though stable for indefinite systems, are computationally more expensive than CG when applied to positive definite matrices. In this paper, we present an iterative method for the case wh...

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approx...