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| Content Provider | Springer Nature Link |
|---|---|
| Author | Conceição, Ana C. Kravchenko, Viktor G. Pereira, José C. |
| Copyright Year | 2012 |
| Abstract | We constructed an algorithm, [SInt], for computing some classes of Cauchy type singular integrals on the unit circle. The design of [SInt] was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithm. Furthermore, we show how the factorization algorithm described in Conceição et al. (2010) allowed us to construct and implement the [SIntAFact] algorithm for calculating several interesting singular integrals that cannot be computed by [SInt]. All the above techniques were implemented using the symbolic computation capabilities of the computer algebra system Mathematica. The corresponding source code of [SInt] is made available in this paper. Several examples of nontrivial singular integrals computed with both algorithms are presented. |
| Ending Page | 288 |
| Page Count | 16 |
| Starting Page | 273 |
| File Format | |
| ISSN | 10197168 |
| e-ISSN | 15729044 |
| Journal | Advances in Computational Mathematics |
| Issue Number | 2 |
| Volume Number | 39 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2012-09-04 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Factorization theory Integration, integrals of Cauchy type, integral representations of analytic functions Numeric Computing Mathematics Theory of Computation Symbolic computation Symbolic computation and algebraic computation Factorization theory (including Wiener-Hopf and spectral factorizations) Spectrum, resolvent Algebra Calculus of Variations and Optimal Control; Optimization Singular integrals Mathematica software system Integral equations with kernels of Cauchy type |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computational Mathematics |
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