TR-2014005: Fast Approximation Algorithms for Computations with Cauchy Matrices and Extensions
Year: 2014
Type: report
Abstract: The papers [MRT05], [CGS07], [XXG12], and [XXCB14] combine the techniques of the Fast Multipole Method of [GR87], [CGR98] with the transformations of matrix structures, traced back to [P90]. The resulting numerically stable algorithms approximate the solutions of Toeplitz, Hankel, Toeplitz-like, and Hankel-like linear systems of equations in nearly linear arithmetic time, versus the classical cubic time and the quadratic time of the previous advanced algorithms.We extend this progress to decrease the arithmetic time of the known numerical algorithms from quadratic to nearly linear for computations with a large class of matrices that have structure of Cauchy or Vandermonde type and for the evaluation and interpolation of polynomials and rational functions.We detail and analyze the new algorithms, and in [Pa] we extend them further.
Author: Victor Y. Pan
Institution: City University of New York
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2198011858