简介：

简介：Westudypreconditioningtechniquesusedinconjunctionwiththeconjugategradientmethodforsolvingmulti-length-scalesymmetricpositivedefinitelinearsystemsoriginatingfromthequantumMonteCarlosimulationofelectroninteractionofcorrelatedmaterials.Existingpreconditioningtechniquesarenotdesignedtobeadaptivetovaryingnumericalpropertiesofthemulti-length-scalesystems.Inthispaper,weproposeahybridincompleteCholesky(HIC)preconditioneranddemonstrateitsadaptivitytothemulti-length-scalesystems.Inaddition,weproposeanextensionofthecompressedsparsecolumnwithrowaccess(CSCR)sparsematrixstorageformattoefficientlyaccommodatethedataaccesspatterntocomputetheHICpreconditioner.Weshowthatformoderatelycorrelatedmaterials,theHICpreconditionerachievestheoptimallinearscalingofthesimulation.Thedevelopmentofalinear-scalingpreconditionerforstronglycorrelatedmaterialsremainsanopentopic.

简介：目前大多数高三数学教师仍然把知识技能作为数学教学的主要目标，教学活动目标单一，拼时间、拼消耗，缺乏对目标全方位的认识和掌控，忽视了诸如思维能力的发展、数学兴趣的培养等其他方面的目标；如何突破教学瓶颈，做到事半功倍？笔者在多年的高三数学课堂教学中，尝试着引导学生体验课堂，形成动态课堂，收到了很好的教学效果．