Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
1-9-2014
Abstract/Description
The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having O(n2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an O(n2) algorithm to compute the inversion of quasiseparable Vandermonde-like matrices.
Publication Title
Cornell University Library
Publisher
Cornell University Library
Scholarly Commons Citation
Perera, S. M., Bonik, G., & Olshevsky, V. (2014). A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices. Cornell University Library, (). Retrieved from https://commons.erau.edu/publication/1038
Included in
Controls and Control Theory Commons, Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Signal Processing Commons, Theory and Algorithms Commons
