Masterclass: singular integrals and orthogonal polynomials
54 mins 37 secs,
248.02 MB,
WebM
640x360,
30.0 fps,
44100 Hz,
620.0 kbits/sec
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About this item
| Description: |
Olver, S
Wednesday 11th December 2019 - 09:00 to 10:00 |
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| Created: | 2019-12-11 10:16 |
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| Collection: | Complex analysis: techniques, applications and computations |
| Publisher: | Isaac Newton Institute |
| Copyright: | Olver, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Orthogonal polynomials are fundamental tools in numerical methods, including for numerical methods for singular integral equations. A known result is that Cauchy transforms of weighted orthogonal polynomials satisfy the same three-term recurrences as the orthogonal polynomials themselves for n > 0. This basic fact leads to extremely effective schemes of calculating singular integrals that converge spectrally fast (faster than any algebraic power), uniformly in the complex plane. Closed formulae for Cauchy transforms on more complicated geometries are derivable using the Plemelj lemma. These techniques extend to other singular integrals such as those with logarithmic kernels. We will demonstrate these results in Julia using ApproxFun.jl and SingularIntegralEquations.jl. |
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| MPEG-4 Video | 640x360 | 1.94 Mbits/sec | 794.99 MB | View | Download | |
| WebM * | 640x360 | 620.0 kbits/sec | 248.02 MB | View | Download | |
| iPod Video | 480x270 | 521.94 kbits/sec | 208.73 MB | View | Download | |
| MP3 | 44100 Hz | 249.78 kbits/sec | 99.98 MB | Listen | Download | |
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