Horner scheme for polynomials

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1: 1.11 Zeros of Polynomials

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Horner’s Scheme

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Extended Horner Scheme

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2: 18.40 Methods of Computation

… ►Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)). …

3: 3.8 Nonlinear Equations

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§3.8(iv) Zeros of Polynomials

►The polynomial … ►After a zero $\zeta$ has been computed, the factor $z-\zeta$ is factored out of $p(z)$ as a by-product of Horner’s scheme (§1.11(i)) for the computation of $p(\zeta )$. … ►For further information on the computation of zeros of polynomials see McNamee (2007). … ►

Example. Wilkinson’s Polynomial

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