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Related Experiment Video

Updated: Mar 1, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

A new localization set for generalized eigenvalues.

Jing Gao¹, Chaoqian Li²

¹Department of Mathematics, Guangzhou Vocational College of Technology & Business, Guangzhou, Guangdong 510000 China.

Journal of Inequalities and Applications

|June 6, 2017

Summary

This summary is machine-generated.

Researchers developed a new localization set for generalized eigenvalues, improving upon existing methods. This tighter set offers more precise estimations for generalized eigenvalue problems in numerical analysis.

Keywords:

generalized eigenvalue inclusion set matrix pencil

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Area of Science:

Numerical Analysis
Linear Algebra

Background:

Generalized eigenvalue problems are fundamental in various scientific and engineering fields.
Existing localization sets for generalized eigenvalues provide bounds but can be improved for tighter estimations.

Purpose of the Study:

To derive a novel localization set for generalized eigenvalues.
To demonstrate that the new set offers a tighter bound compared to previously established results.

Main Methods:

Development of a new localization technique for generalized eigenvalues.
Comparative analysis of the new localization set against existing ones from the literature.

Main Results:

A new localization set for generalized eigenvalues has been successfully obtained.
The newly derived set is proven to be tighter than the localization set presented in Numer. Linear Algebra Appl. 16:883-898, 2009.
Numerical examples confirm the improved accuracy and validity of the results.

Conclusions:

The new localization set provides a more refined region for generalized eigenvalues.
This advancement contributes to more accurate computations in numerical linear algebra.
The findings are validated through numerical experiments, underscoring their practical relevance.