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Title: Structured matrix methods for a polynomial root solver using approximate greatest common divisor computations and approximate polynomial factorisations
Author: Lao, Xinyuan
ISNI:       0000 0004 2708 462X
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2011
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available