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Pan, V.Y., Zheng, A., Huany, X. and Yu, Y. (1995) Fast Multipoint Polynomial Evaluation and Interpolation via Computation with Structured Matrices. Annals of Numerical Mathematics, 4, 483-510.

has been cited by the following article:

• TITLE: Fast and Numerically Stable Approximate Solution of Trummer’s Problem

  AUTHORS: Mohammad M. Tabanjeh

  KEYWORDS: Cauchy Matrix, Mulipoint Algorithm, Structure Matrices, Displacement Operators

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.4 No.5, November 11, 2014

  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.