Adaptive methods for nonlinear eigenvalue problems with parameters

带参数的非线性特征值问题的自适应方法

• 批准号: 244622119
• 负责人: Dr. Agnieszka Miedlar
• 金额: --
• 依托单位: Mathematics Institute for Geometry and Applications (MATHGEOM)
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/244622119?language=en
• 关键词: Adaptive; methods; nonlinear; eigenvalue; problems

This project is concerned with adaptive methods for nonlinear eigenvalue problems that are nonlinear in the eigenvalue parameter. Many problems of this type arise from the discretization of differential and integral equations. Furthermore, very often they depend on additional parameters. The proposed research aims to fill the gap in understanding and improving discretization processes and design a robust numerical methods to solve the resulting discretized problems efficiently. To address these research objectives the project will incorporate expertise from the spectral and perturbation theory, variational characterizations, preconditioned iterative methods, continuation methods and a posteriori error analysis.

本计画主要研究非线性特征值问题的自适应方法，这些问题的特征值参数是非线性的。许多这类问题都是由微分和积分方程的离散化引起的。此外，它们通常取决于附加参数。本研究的目的在于填补离散化过程中的差距，并设计一种稳健的数值方法来有效地解决离散化问题。为了解决这些研究目标，该项目将结合专业知识，从频谱和扰动理论，变分表征，预处理迭代方法，连续方法和后验误差分析。

项目成果

An algorithm for computing minimal Geršgorin sets

一种计算最小GerÅ¡gorin集的算法

• DOI: 10.1002/nla.2024
• 发表时间: 2016
• 期刊: Numerical Linear Algebra with Applications
• 影响因子: 4.3
• 作者: V. Kostić;A. Międlar;Lj. Cvetković
• 通讯作者: Lj. Cvetković