Embree, Mark and Trefethen, Lloyd N. (1998) Green's functions for multiply connected domains via conformal mapping. Technical Report. SIAM. (Submitted)

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Abstract
A method is described for the computation of the Green's function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a SchwarzChristoffel conformal map of the part of the upper halfplane exterior to the problem domain onto a semiinfinite strip whose end contains K1 slits. From the Green's function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iteration. By making the end of the strip jagged, the method can be generalised to weighted Green's functions and weighted approximations.
Item Type:  Technical Report (Technical Report) 

Subjects:  O  Z > Potential theory A  C > Approximations and expansions D  G > Functions of a complex variable H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1298 
Deposited By:  Lotti Ekert 
Deposited On:  04 Jun 2011 08:15 
Last Modified:  29 May 2015 18:59 
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