New Convergence Mode For Generalized Spectrum Approximation

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2022-12-08 DOI:10.1134/s1995423922040061

S. Kamouche, H. Guebbai

引用次数: 0

Abstract

In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known \(\nu\)-convergence used in the case of classical spectrum approximation. This new vision allows us to see the \(\nu\)-convergence assumption as a special case of our new method compared to the hypotheses needed in the old methods, those required in this paper are weaker. In addition, we prove that the property \(U\) holds, which solves a spectral pollution problem arising in the spectrum approximation of unbounded operators.

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广义谱近似的新收敛模式

摘要本文引入一种新的收敛模式来处理两个有界算子的广义谱逼近问题。这种新技术是通过推广经典谱近似中使用的著名的\(\nu\) -收敛得到的。这个新的视角让我们看到\(\nu\) -收敛假设是我们新方法的一个特例，与旧方法中需要的假设相比，本文中需要的假设更弱。此外，我们还证明了\(U\)的成立，从而解决了无界算子的谱逼近中出现的谱污染问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.