White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Structured matrix methods for a polynomial root solver using approximate greatest common divisor computations and approximate polynomial factorisations.

Lao, Xinyuan (2011) Structured matrix methods for a polynomial root solver using approximate greatest common divisor computations and approximate polynomial factorisations. PhD thesis, University of Sheffield.

[img] Text (543782.pdf)
543782.pdf

Download (21Mb)

Abstract

This thesis discusses the use of structure preserving matrix methods for the numerical approximation of all the zeros of a univariate polynomial in the presence of noise. In particular, a robust polynomial root solver is developed for the calculation of the multiple roots and their multiplicities, such that the knowledge of the noise level is not required. This designed root solver involves repeated approximate greatest common divisor computations and polynomial divisions, both of which are ill-posed computations. A detailed description of the implementation of this root solver is presented as the main work of this thesis. Moreover, the root solver, implemented in MATLAB using 32-bit floating point arithmetic, can be used to solve non-trivial polynomials with a great degree of accuracy in numerical examples.

Item Type: Thesis (PhD)
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Computer Science (Sheffield)
The University of Sheffield > Faculty of Science (Sheffield) > Computer Science (Sheffield)
Identification Number/EthosID: uk.bl.ethos.543782
Depositing User: EThOS Import Sheffield
Date Deposited: 31 May 2016 13:47
Last Modified: 31 May 2016 13:47
URI: http://etheses.whiterose.ac.uk/id/eprint/12818

Actions (repository staff only: login required)