Fast and Numerically Stable Approximate Solution of Trummer’s Problem ()
ABSTRACT
Trummer’s problem is the problem of multiplication of an n × n Cauchy matrix C by a vector. It
serves as the basis for the solution of several problems in scientific
computing and engineering [1]. The
straightforward algorithm solves Trummer’s problem in O(n2) flops.
The fast algorithm solves the problem in O(nlog2n) flops [2] but has poor
numerical stability. The algorithm we discuss here in this paper is the
celebrated multipoint algorithm [3] which has been
studied by Pan et al. The algorithm approximates the solution in O(nlogn) flops in terms of n but its cost estimate depends on the
bound of the approximation error and also depends on the correlation between
the entries of the pair of n-dimensional
vectors defining the input matrix C.
Share and Cite:
Tabanjeh, M. (2014) Fast and Numerically Stable Approximate Solution of Trummer’s Problem.
American Journal of Computational Mathematics,
4, 387-395. doi:
10.4236/ajcm.2014.45033.
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