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From |
Hua Peng <hpeng@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: mata polyroots issue |

Date |
Mon, 11 May 2009 12:39:15 -0500 |

Lirac<lirac271@yahoo.com> asked a question about mata function polyroot(): >I am running Stata 10.1 on Mac OS 10.4. The following issue is perplexing me: > >------- >mata: >mata clear >polynomial1 = (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-30,29) >polyeval(polynomial1,1) >polyroots(polynomial1) >------- > >The polyeval line makes it clear that x=1 is a root for this polynomial. >However, 1 is not a reported result for polyroots. The first two results reported by polyroots(polynomial1) are (1-1.1729e-08i, 1+1.1729e-08i). The results are correct. Notice polynomial1 can be factored into (x-1)*(29*x^29 - x^28 - x^27 - x^26 -... - 1), and the second term is 0 at x=1. Hence polynomial has a factor (x-1)^2, i.e., 1 is a double root of polynomial1. Mata correctly identifies this. Due to numerical round-off, Mata computes the degree two factor as (x-1)^2+e, where e is a small positive number, instead of exact (x-1)^2, and consequently Mata reports two complex conjugate roots close to 1 instead of two 1. >What is odd is that >if I add or subtract a zero term to the polynomial, polyroots() will >then correctly report x=1 as a root. i.e., the following works: > >polynomial2 = (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-30,29) >polynomial3 = (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-30,>29) > >Does anybody know what is going on here? > Both polynomial2 and polynomial3 have only (x-1) factor. Mata correctly reports 1 as a simple root. --Hua (hpeng@stata.com) * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: mata polyroots issue***From:*John Bates <lirac271@yahoo.com>

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