椭圆算子finite difference逼近矩阵序列的谱估计和模估计
Spectral and norm estimates for matrix sequences arising from a finite difference approximation of elliptic operators
摘要：
当近似椭圆问题使用专门的近似技术，我们得到大型结构矩阵的分析提供了信息的稳定性的方法。在这里，我们提供谱和范数估计所产生的近似拉普拉斯通过特设有限差分矩阵序列。分析涉及几个工具，从矩阵理论，特别是从设置的Toeplitz运营商和广义局部Toeplitz矩阵序列。数值实验结果验证了理论分析的正确性。
英文摘要：
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for matrix sequences arising from the approximation of the Laplacian via ad hoc finite differences. The analysis involves several tools from matrix theory and in particular from the setting of Toeplitz operators and Generalized Locally Toeplitz matrix sequences. Several numerical experiments are conducted, which confirm the correctness of the theoretical findings.
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