Numerical Methods for Roots of Polynomials

Download or Read online Numerical Methods for Roots of Polynomials full in PDF, ePub and kindle. This book written by J.M. McNamee and published by Elsevier which was released on 17 August 2007 with total pages 354. We cannot guarantee that Numerical Methods for Roots of Polynomials book is available in the library, click Get Book button to download or read online books. Join over 650.000 happy Readers and READ as many books as you like.

Numerical Methods for Roots of Polynomials
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Publisher : Elsevier
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ISBN : 0080489478
Pages : 354 pages
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Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled “A Handbook of Methods for Polynomial Root-finding . This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades Gives description of high-grade software and where it can be down-loaded Very up-to-date in mid-2006; long chapter on matrix methods Includes Parallel methods, errors where appropriate Invaluable for research or graduate course

Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to

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Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method,

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Numerical Methods for Roots of Polynomials   Part II

Download or read online Numerical Methods for Roots of Polynomials Part II written by J.M. McNamee,V.Y. Pan, published by Elsevier Inc. Chapters which was released on 2013-07-19. Get Numerical Methods for Roots of Polynomials Part II Books now! Available in PDF, ePub and Kindle.

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Numerical Methods for Roots of Polynomials   Part II

The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average

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Numerical Methods for Roots of Polynomials   Part II

This chapter treats several topics, starting with Bernoulli’s method. This method iteratively solves a linear difference equation whose coefficients are the same as those of the polynomial. The ratios of successive iterates tends to the root of largest magnitude. Special versions are used for complex and/or multiple roots.

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Numerical Methods for Roots of Polynomials   Part II

First we consider the Jenkins–Traub 3-stage algorithm. In stage 1 we defineIn the second stage the factor is replaced by for fixed , and in the third stage by where is re-computed at each iteration. Then a root. A slightly different algorithm is given for real polynomials. Another class of methods

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Numerical Methods for Roots of Polynomials

Download or read online Numerical Methods for Roots of Polynomials written by J. M. McNamee, published by Unknown which was released on 2007. Get Numerical Methods for Roots of Polynomials Books now! Available in PDF, ePub and Kindle.

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Numerical Methods for Roots of Polynomials   Part II

In considering the stability of mechanical systems we are led to the characteristic equation . Continuous-time systems are stable if all the roots of this equation are in the left half-plane (Hurwitz stability), while discrete-time systems require all (Schur stability). Hurwitz stability has been treated by the Cauchy index and Sturm

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Numerical Methods for Roots of Polynomials   Part II

We consider proofs that every polynomial has one zero (and hence n) in the complex plane. This was proved by Gauss in 1799, although a flaw in his proof was pointed out and fixed by Ostrowski in 1920, whereas other scientists had previously made unsuccessful attempts. We give details of Gauss’ fourth (

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Numerical Methods for Roots of Polynomials   Part II

We deal here with low-degree polynomials, mostly closed-form solutions. We describe early and modern solutions of the quadratic, and potential errors in these. Again we give the early history of the cubic, and details of Cardan’s solution and Vieta’s trigonometric approach. We consider the discriminant, which decides what

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Numerical Methods for Roots of Polynomials   Part II

We discuss the secant method:where are initial guesses. In the Regula Falsi variation we start with initial guesses and such that ; after an iteration similar to the above we replace either a or b by the new value depending on which of or has the same sign as . Often

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Numerical Methods for Roots of Polynomials   Part II

Whereas Newton’s method involves only the first derivative, methods discussed in this chapter involve the second or higher. The “classical” methods of this type (such as Halley’s, Euler’s, Hansen and Patrick’s, Ostrowski’s, Cauchy’s and Chebyshev’s) are all third order with three evaluations, so

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Numerical Methods for Roots of Polynomials   Part II

We discuss Graeffes’s method and variations. Graeffe iteratively computes a sequence of polynomialsso that the roots of are those of raised to the power . Then the roots of can be expressed in terms of the coefficients of . Special treatment is given to complex and/or multiple modulus roots. A

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Numerical Methods for Engineers and Scientists

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative

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Some Numerical Methods for Locating Roots of Polynomials

Download or read online Some Numerical Methods for Locating Roots of Polynomials written by Thornton Carle Fry, published by Unknown which was released on 1945*. Get Some Numerical Methods for Locating Roots of Polynomials Books now! Available in PDF, ePub and Kindle.

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