Methods for finding Zeros in Polynomials
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776819002
Table of contents: title: Content; title: 1. Introduction; title: 2. Complex polynomials in general; title: 2.1. Polynomials in one variable; title: 2.2. Transformations of real polynomials; title: 2.3. The fundamental theorem of algebra; title: 2.4. Vieti’s formulæ; title: 2.5. Rolle’s theorems; title: 3. Some solution formulæ of roots of polynomials; title: 3.1. The binomial equation; title: 3.2. The equation of second degree; title: 3.3. Rational roots; title: 3.4. The Euclidean algorithm; title: 3.5. Roots of multiplicity > 1; title: 4. Position of roots of polynomials in the complex plane; title: 4.1. Complex roots of a real polynomial; title: 4.2. Descartes’s theorem; title: 4.3. Fourier-Budan’s theorem; title: 4.4. Sturm’s theorem; title: 4.5. Rouch´e’s theorem; title: 4.6. Hurwitz polynomials; title: 5. Approximation methods; title: 5.1. Newton’s approximation formula; title: 5.2. Graeffe’s root-squaring process; title: 6. Appendix; title: 6.1. The binomial formula; title: 6.2. The identity theorem for convergent power series; title: 6.3. Taylor’s formula; title: 6.4. Weierstraß’s approximation theorem; title: 7. Index