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Calculating real roots using Chebyshev polynomials

Blaž Oven (2016) Calculating real roots using Chebyshev polynomials. EngD thesis.

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    In this work, Chebyshev polynomials of the first and the second kind, their properties and the Chebyshev series will be examined. We will use Chebyshev polynomials of the first kind to find roots of the smooth function f on the given interval. At first the function will be approximated and then the polynomial root-finders on the truncated Chebyshev series will be used. In the next chapter we will study how to find roots of a polynomial function on the interval which we will, with some algorithms, divide on subintervals with the purpose of more accurate and faster finding of the roots. Different algorithms and their use, their complexity and their strengths and weaknesses will be presented. During this work we have also programmed these algorithms in Matlab. We will show their practical application on some examples.

    Item Type: Thesis (EngD thesis)
    Keywords: roots, Chebyshev polynomials, Chebyshev series, Convert to powers, Degree doubling
    Number of Pages: 47
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    izr. prof. dr. Marjetka KrajncMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1536776899)
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 3239
    Date Deposited: 05 Feb 2016 14:25
    Last Modified: 19 Feb 2016 09:07
    URI: http://eprints.fri.uni-lj.si/id/eprint/3239

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