NDLI: Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Schneider, Claus B.
Copyright Year	1998
Abstract	A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.
Starting Page	71
Ending Page	77
Page Count	7
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142995285149
e-ISSN	10957170
Issue Number	1
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Hilbert transform integral equations boundary element method Integral equations Moore--Penrose inverse Special transforms Integral equations with kernels of Cauchy type boundary integrals
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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