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| Content Provider | Springer Nature Link |
|---|---|
| Author | Conceição, Ana C. Pereira, José C. |
| Copyright Year | 2016 |
| Abstract | Spectral theory has many applications in several main scientific research areas (structural mechanics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and the importance of its study is globally acknowledged. In recent years, several software applications were made available to the general public with extensive capabilities of symbolic computation. These applications, known as computer algebra systems (CAS), allow to delegate to a computer all, or a significant part, of the symbolic calculations present in many mathematical algorithms. In our work we use the CAS Mathematica to implement for the first time on a computer analytical algorithms developed by us and others within the Operator Theory. The main goal of this paper is to show how the symbolic computation capabilities of Mathematica allow us to explore the spectra of several classes of singular integral operators. For the one-dimensional case, nontrivial rational examples, computed with the automated process called [ASpecPaired-Scalar], are presented. For the matrix case, nontrivial essentially bounded and rational examples, computed with the analytical algorithms [AFact], [SInt], and [ASpecPaired-Matrix], are presented. In both cases, it is possible to check, for each considered paired singular integral operator, if a complex number (chosen arbitrarily) belongs to its spectrum. |
| Starting Page | 291 |
| Ending Page | 309 |
| Page Count | 19 |
| File Format | |
| ISSN | 16618270 |
| Journal | Mathematics in Computer Science |
| Volume Number | 10 |
| Issue Number | 2 |
| e-ISSN | 16618289 |
| Language | English |
| Publisher | Springer International Publishing |
| Publisher Date | 2016-04-12 |
| Publisher Place | Cham |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Spectral algorithms Factorization algorithms Paired singular integral operators Essentially bounded matrix functions Rational matrix functions Wolfram Mathematica Integral operators Factorization theory Symbolic computation and algebraic computation Mathematics Computer Science |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computational Theory and Mathematics Computational Mathematics |
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