A new Gershgorin-type result for the localisation of the spectrum of matrices

DallAcqua Anna; Mugnolo Delio; Schelling Michael

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A new Gershgorin-type result for the localisation of the spectrum of matrices

机译：矩阵光谱定位的新Gershgorin型结果

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摘要

We present a Gershgorin's type result on the localisation of the spectrum of a matrix. Our method is elementary as it relies upon the method of Schur complements, but it outperforms the one based on the Cassini ovals of Ostrovski and Brauer. Furthermore, it yields estimates that hold without major differences in the cases of both scalar and operator matrices. Several refinements of known results are obtained. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Wentheim

机译：我们在矩阵光谱的定位上给出了格什哥林类型的结果。我们的方法是基本的，因为它依赖于Schur补数的方法，但是它优于基于Ostrovski和Brauer的Cassini椭圆的方法。此外，它得出的估计值在标量和运算符矩阵的情况下都没有太大差异。获得了一些已知结果的改进。（C）2015 WILEY-VCH Verlag GmbH＆Co.KGaA，Wentheim

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《Mathematische Nachrichten》 |2015年第18期|共14页
作者
DallAcqua Anna; Mugnolo Delio; Schelling Michael;
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正文语种 eng
中图分类数学;
关键词
Estimates of the spectrum of matrices; operator matrices of unbounded operators;

机译：矩阵谱的估计;无界算子的算子矩阵;

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A new Gershgorin-type result for the localisation of the spectrum of matrices

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