A parallel version of a fast algorithm for singular integral transforms

The mathematical foundation of an algorithm for fast and accurate evaluation of singular integral transforms was given by Daripa [9,10,12]. By construction, the algorithm offers good parallelization opportunities and a lower computational complexity when compared with methods based on quadrature rules. In this paper we develop a parallel version of the fast algorithm by redefining the inherently sequential recurrences present in the original sequential formulation. The parallel version only utilizes a linear neighbor-to-neighbor communication path, which makes the algorithm very suitable for any distributed memory architecture. Numerical results and theoretical estimates show good parallel scalability of the algorithm. This revised version was published online in June 2006 with corrections to the Cover Date.