On the application of GMRES to oscillatory singular integral equations
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0502-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0502-4 | ||
| 100 | 1 | |a Trogdon |D Thomas |u Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., 10012, New York, NY, USA |4 aut | |
| 245 | 1 | 0 | |a On the application of GMRES to oscillatory singular integral equations |h [Elektronische Daten] |c [Thomas Trogdon] |
| 520 | 3 | |a We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from a new formula for the Cauchy integral of a rational function with an oscillatory exponential factor. The inner product of such functions is also computed explicitly. With these tools in hand, the GMRES algorithm is applied to both non-oscillatory and oscillatory singular integral equations. In specific cases, ideas from Fredholm theory and Riemann-Hilbert problems are used to motivate preconditioners for these singular integral equations. A significant acceleration in convergence is realized for these examples. This presents a useful link between the theory of singular integral equations and the numerical analysis of such equations. Furthermore, this method presents a first step towards a solver for the inverse scattering transform that does not require the deformation of a Riemann-Hilbert problem. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Singular integral equations |2 nationallicence | |
| 690 | 7 | |a Oscillatory quadrature |2 nationallicence | |
| 690 | 7 | |a Riemann-Hilbert problems |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 591-620 |x 0006-3835 |q 55:2<591 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0502-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0502-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Trogdon |D Thomas |u Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., 10012, New York, NY, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 591-620 |x 0006-3835 |q 55:2<591 |1 2015 |2 55 |o 10543 | ||