Numerical Methods for Roots of Polynomials - Part II

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  Numerical Methods for Roots of Polynomials - Part II: Introduction

  By J.M. McNamee, V.Y. Pan

  Numerical Methods for Roots of Polynomials - Part II: Introduction

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 15. Nearly Optimal Universal Polynomial Factorization and Root-Finding

  By J.M. McNamee, V.Y. Pan

  The zeros of a polynomial can be readily recovered from its linear factors.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 13. Existence and Solution by Radicals

  By J.M. McNamee, V.Y. Pan

  We consider proofs that every polynomial has one zero (and hence n) in the complex plane.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 11. Jenkins–Traub, Minimization, and Bairstow Methods

  By J.M. McNamee, V.Y. Pan

  First we consider the Jenkins–Traub 3-stage algorithm.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 10. Bernoulli, Quotient-Difference, and Integral Methods

  By J.M. McNamee, V.Y. Pan

  This chapter treats several topics, starting with Bernoulli’s method.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 14. Stability Considerations

  By J.M. McNamee, V.Y. Pan

  In considering the stability of mechanical systems we are led to the characteristic equation .

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 12. Low-Degree Polynomials

  By J.M. McNamee, V.Y. Pan

  We deal here with low-degree polynomials, mostly closed-form solutions.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 7. Bisection and Interpolation Methods

  By J.M. McNamee, V.Y. Pan

  We discuss the secant method:where are initial guesses.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 9. Methods Involving Second or Higher Derivatives

  By J.M. McNamee, V.Y. Pan

  Whereas Newton’s method involves only the first derivative, methods discussed in this chapter involve the second or higher.

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  Numerical Methods for Roots of Polynomials - Part II: Chapter 8. Graeffe’s Root-Squaring Method

  By J.M. McNamee, V.Y. Pan

  We discuss Graeffes’s method and variations.