Analysis of two-grid methods: The nonnormal case
Analysis of two-grid methods: The nonnormal case
复制标题
双网格方法分析：非正态情况
作者：
Y. Notay
将双网格法代数分析的核心结果推广到迭代矩阵值域（或数值范围）的边界关系中。在此基础上，得到了它的范数和数值半径的界，得到了严格的收敛估计。数值实例表明，理论结果提供了较好的定性预测，使人们能够预测两网格方法的成功或失败。它们还表明，值场和相关的数值半径是比特征值分布和相关的谱半径更可靠的收敛指标。在此基础上，讨论了局部傅立叶分析和局部模态分析在非对称问题中的作用。
Core results about the algebraic analysis of two-grid methods are extended in relations bounding the field of values (or numerical range) of the iteration matrix. On this basis, bounds are obtained on its norm and numerical radius, leading to rigorous convergence estimates. Numerical illustrations show that the theoretical results deliver qualitatively good predictions, allowing one to anticipate success or failure of the two-grid method. They also indicate that the field of values and the associated numerical radius are much more reliable convergence indicators than the eigenvalue distribution and the associated spectral radius. On this basis, some discussion is developed about the role of local Fourier or local mode analysis for nonsymmetric problems.