LinBairstow algorithm for Polynomial Roots

02222022, 11:02 PM
(This post was last modified: 03022022 01:57 AM by Thomas Klemm.)
Post: #4




RE: LinBairstow algorithm for Polynomial Roots
(11C) Bairstow's Method explains the algorithm and gives an example.
Using Optimization to Extract Roots of Real Coefficient Polynomials is an older post by Namir with Matlab programs. There are links to other algorithms, among them the DurandKerner method. In an earlier thread I mentioned Polynomials for the HP41 where you can find Quadratic factors which also uses Bairstow's method. There I also mentioned an article in PRISMA, the magazine of the former CCD, where I first came across this method. Thanks to Jürgen Keller and Martin Hepperle I finally found it in the collection of the PRISMA Zeitschriften 1982 – 1992:
Recently Robert van Engelen wrote programs for both the Aberth method and the Weierstrass / DurandKerner method. Example \(P(x)=2x^59x^4+15x^3+65x^2267x+234=0\) Start the Program Code: XEQ "LINBST" Insert the Coefficients Code: A<0>? Initialize the Guesses Code: R INIT? Results Code: R1=2.00000 Summary Factors \(2x^59x^4+15x^3+65x^2267x+234=\) \((x^2+1.5x4.5)(x^24x+13)(2x4)=\) \((x1.5)(x+3)(x^24x+13)2(x2)=\) \((2x3)(x2)(x+3)(x^24x+13)\) Solutions \(x_1=2\) \(x_2=1.5\) \(x_3=2+3i\) \(x_5=23i\) \(x_5=3\) 

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Messages In This Thread 
LinBairstow algorithm for Polynomial Roots  Namir  02162022, 12:56 PM
RE: LinBairstow algorithm for Polynomial Roots  floppy  02212022, 11:53 AM
RE: LinBairstow algorithm for Polynomial Roots  Namir  02212022, 10:18 PM
RE: LinBairstow algorithm for Polynomial Roots  Thomas Klemm  02222022 11:02 PM
RE: LinBairstow algorithm for Polynomial Roots  robve  02232022, 06:31 PM

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