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.
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.
Metadata
Awarding institution: | University of Sheffield |
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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 |
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