Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples
A numerical method for computing zeros of analytic complex functions is presented. It relies on Cauchy's residue theorem and the method of Newton's identities, which translates the problem to finding zeros of a polynomial. In order to stabilize the numerical algorithm, formal orthogonal po...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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VSB-Technical University of Ostrava
2017-01-01
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| Series: | Advances in Electrical and Electronic Engineering |
| Subjects: | |
| Online Access: | http://advances.utc.sk/index.php/AEEE/article/view/2252 |
| _version_ | 1827947493584797696 |
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| author | Erika Strakova Dalibor Lukas Petr Vodstrcil |
| author_facet | Erika Strakova Dalibor Lukas Petr Vodstrcil |
| author_sort | Erika Strakova |
| collection | DOAJ |
| description | A numerical method for computing zeros of analytic complex functions is presented. It relies on Cauchy's residue theorem and the method of Newton's identities, which translates the problem to finding zeros of a polynomial. In order to stabilize the numerical algorithm, formal orthogonal polynomials are employed. At the end the method is adapted to finding eigenvalues of a matrix pencil in a bounded domain in the complex plane. This work is based on a series of papers of Professor Sakurai and collaborators. Our aim is to make their work available by means of a systematic study of properly chosen examples. |
| first_indexed | 2024-04-09T12:40:50Z |
| format | Article |
| id | doaj.art-7b296c78e40345f98527aae62e2c74c3 |
| institution | Directory Open Access Journal |
| issn | 1336-1376 1804-3119 |
| language | English |
| last_indexed | 2024-04-09T12:40:50Z |
| publishDate | 2017-01-01 |
| publisher | VSB-Technical University of Ostrava |
| record_format | Article |
| series | Advances in Electrical and Electronic Engineering |
| spelling | doaj.art-7b296c78e40345f98527aae62e2c74c32023-05-14T20:50:11ZengVSB-Technical University of OstravaAdvances in Electrical and Electronic Engineering1336-13761804-31192017-01-0115228629510.15598/aeee.v15i2.2252898Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in ExamplesErika Strakova0Dalibor Lukas1Petr Vodstrcil2Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava 708 33, Czech RepublicDepartment of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava 708 33, Czech Republic & IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava, Studentska 6231/1B, Ostrava 708 33, Czech RepublicDepartment of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 17. listopadu 15/2172, Ostrava 708 33, Czech RepublicA numerical method for computing zeros of analytic complex functions is presented. It relies on Cauchy's residue theorem and the method of Newton's identities, which translates the problem to finding zeros of a polynomial. In order to stabilize the numerical algorithm, formal orthogonal polynomials are employed. At the end the method is adapted to finding eigenvalues of a matrix pencil in a bounded domain in the complex plane. This work is based on a series of papers of Professor Sakurai and collaborators. Our aim is to make their work available by means of a systematic study of properly chosen examples.http://advances.utc.sk/index.php/AEEE/article/view/2252contour integral methodformal orthogonal polynomialsgeneralized eigenvalue problemzeros of analytic functions. |
| spellingShingle | Erika Strakova Dalibor Lukas Petr Vodstrcil Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples Advances in Electrical and Electronic Engineering contour integral method formal orthogonal polynomials generalized eigenvalue problem zeros of analytic functions. |
| title | Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples |
| title_full | Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples |
| title_fullStr | Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples |
| title_full_unstemmed | Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples |
| title_short | Finding Zeros of Analytic Functions and Local Eigenvalue Analysis Using Contour Integral Method in Examples |
| title_sort | finding zeros of analytic functions and local eigenvalue analysis using contour integral method in examples |
| topic | contour integral method formal orthogonal polynomials generalized eigenvalue problem zeros of analytic functions. |
| url | http://advances.utc.sk/index.php/AEEE/article/view/2252 |
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