The AAAtrig algorithm for rational approximation of periodic functions
| Title: | The AAAtrig algorithm for rational approximation of periodic functions |
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| Authors: | Baddoo, Peter J. |
| Publication Year: | 2020 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Numerical Analysis |
| More Details: | We present an extension of the AAA (adaptive Antoulas--Anderson) algorithm for periodic functions, called 'AAAtrig'. The algorithm uses the key steps of AAA approximation by (i) representing the approximant in (trigonometric) barycentric form and (ii) selecting the support points greedily. Accordingly, AAAtrig inherits all the favourable characteristics of AAA and is thus extremely flexible and robust, being able to consider quite general sets of sample points in the complex plane. We consider a range of applications with particular emphasis on solving Laplace's equation in periodic domains and compressing periodic conformal maps. These results reproduce the tapered exponential clustering effect observed in other recent studies. The algorithm is implemented in Chebfun. Comment: 20 pages, 6 figures, submitted to SISC |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2008.05446 |
| Accession Number: | edsarx.2008.05446 |
| Database: | arXiv |
| Description not available. |