项目名称: 二次特征值问题的数值求解算法研究
项目编号: No.11461046
项目类型: 地区科学基金项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 汪祥
作者单位: 南昌大学
项目金额: 36万元
中文摘要: 二次特征值的数值求解问题出现在工程和物理许多应用领域,如结构力学中的动力分析、电信仿真、信号处理、微电子力学的建模、声波系统动力学分析等,是当今大规模科学与工程计算所遇到的挑战之一。在本项目中,我们将做如下研究工作:将研究二次特征值问题的线性化技术与广义特征值问题的数值求解方法结合起来,研究基于线性化技术的求解二次特征值问题的高效算法;通过对Krylov子空方法的研究,探索和选取适用于二次特征值投影算法的Krylov子空间,设计针对原问题的直接投影算法;利用二次特征值问题的特殊结构,改进现有的相关算法,设计出快速且稳定的保结构求解算法;在研究二次特征值问题的基础上,将相关理论成果及算法设计思想推广到多项式特征值问题的数值求解中。
中文关键词: 迭代算法;特征值问题;二次特征值问题
英文摘要: A wide variety of applications require the solution of a quadratic eigenvalue problem (QEP), most of them arising in the dynamic analysis of structural mechanical, acoustic systesm, electrical circuit simulation, fluid mechanics, and modeling microelectronic mechanical systems. QEPs also have intersting applications in linear algebra problems and signal processing. Now, QEPs have become one of challenges for large scale of scientific and engineering computation. In this project, we will do the following studies: Firstly, combining the linearization methods for solving quadratic eigenvalue problems with the numerical methods for generalized eigenvalue problem, we will study the efficient algorithms based on linearization methods for quadratic eigenvalue problems; Secondly, we will investigate and choose appropriate Krylove subspace for quadratic eigenvalue projection algorithm and devise some projection algorithms for original problem, by studying Krylov subspace methods; Thirdly, we will improve and generalize the existing methods for QEPs and propose some fast and stable structure preserving algorithms, based on the special structure of QEPs; Finally, based on the study for QEPs, we hope to obtain some efficient methods for polynomial eigenvalue problems (PEPs) by generalizing the theoretical results and the idea of algorithms for QEPs.
英文关键词: iteration algorithms;eigenvalue problems;quadratic eigenvalue problems