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# Solving multiple-root polynomials 1.0

Date Added: April 13, 2013  |  Visits: 234

The MATLAB script file M_polyroots.m is to compute all the roots with multiplicities of any given polynomials. Let a given polynomial p(x) be expressed as p(x) = x^9 +7x^8 +12x^7 -12x^6 -42x^5 -6x^4 +44x^3 +20x^2 -15x -9 = (x +3)^2 * (x +1)^4 * (x -1)^3 = (x^2 +2x -3)^2 * (x +1)^3 * (x^2 -1)It does give, respectively, c = [ +1 +7 +12 -12 -42 -6 +44 +20 -15 -9 ] r = [ -3 -3 -1 -1 -1 -1 +1 +1 +1 ] A = [ 2 -3 +2 +1; 3 +1 +1 +0; 1 -1 +0 +1 ]Then the polynomial coefficient vector p may be created by either (1) p = c (2) p = poly(r) (3) p = polyget(A)The desired roots/mults Z are therefore computed from p by Z = polyroots(p) ******************************************************************************************** For detail description and typical examples, please see attached file: SolvingMultipleRootsPolynomials.pdfThe stand-alone file M_polyroots.exe has also been created to be run in DOS without MATLAB.Request for 'M_polyroots.exe' may be made by e-mail to: fcchang007@yahoo.com.Ref: IEEE Antennas & Propagation Magazine, vol. 51, no. 6, pp.151-155, Dec 2009*****************************************************************************************

 Requirements: No special requirements Platforms: Matlab Keyword: Attached,  Computed,  Description,  Detail,  Examples,  Polyrootsp,  Rootsmults,  Typical Users rating: 0/10

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