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A fast algorithm for Trummer’s problem. (English) Zbl 0618.65030

The authors describe a fast algorithm for the evaluation of By, where \(B=(b_{ij})\) with \(b_{ij}=(c_ i-c_ j)^{-1}\) (i\(\neq j)\) and \(b_{ii}=0\), and where y is an arbitrary n-vector. This problem occurs, for example, in numerical conformal mapping. The algorithm produces By in \({\mathcal O}(n(\log n)^ 2)\) time and needs \({\mathcal O}(n\log n)\) space. In special instances, the time can even be reduced to \({\mathcal O}(n \log n)\).
Reviewer: D.Gaier

MSC:

65F30 Other matrix algorithms (MSC2010)
68Q25 Analysis of algorithms and problem complexity
30C30 Schwarz-Christoffel-type mappings

Citations:

Zbl 0596.30013
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