Article View: sci.math.num-analysis
Article #411Re: Roots of equations Was: Newton Raphsons iteration method
From: Roger Alexander
Date: Thu, 03 Sep 1992 12:57
Date: Thu, 03 Sep 1992 12:57
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1526 bytes
In <SMITH.92Sep2103757@minerva.harvard.edu> smith@minerva.harvard.edu (Steven Smith) writes: >alex@iastate.edu (Roger Alexander) writes: >> Not so. The solutions of the equation are isolated (implicit >> function theorem) but there may be infinitely many. Let >> >> g(x,y) = (exp(x)cos(y)-1, exp(x) sin(y)). >> >> Then det g' = exp(2x) != 0 anywhere, but g(0,2*Pi*n) = 0 for every >> integer n. > [...] The example x -> sin x works too. This function is not an example because the derivative has a zero. -- *_________________* "Faculty members encourage the free pursuit of Roger Alexander | learning in their students and protect academic alex@iastate.edu | freedom of students." --ISU Faculty Handbook *_________________* [official statement of policies & procedures]
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arc1-ca.pugleaf.net!sparky!uunet!haven.umd.edu!darwin.sura.net!zaphod.mps.ohio-state.edu!moe.ksu.ksu.edu!ux1.cso.uiuc.edu!news.iastate.edu!pv3448.vincent.iastate.edu!alexReferences:
<1992Sep1.094300.2414@nuscc.nus.sg> <SMITH.92Sep1154327@minerva.harvard.edu> <alex.715433129@pv3448.vincent.iastate.edu> <SMITH.92Sep2103757@minerva.harvard.edu>Show Full Headers
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Newsgroups: sci.math.num-analysis Path: arc1-ca.pugleaf.net!sparky!uunet!haven.umd.edu!darwin.sura.net!zaphod.mps.ohio-state.edu!moe.ksu.ksu.edu!ux1.cso.uiuc.edu!news.iastate.edu!pv3448.vincent.iastate.edu!alex From: alex@iastate.edu (Roger Alexander) Subject: Re: Roots of equations Was: Newton Raphsons iteration method Message-ID: <alex.715525035@pv3448.vincent.iastate.edu> Sender: news@news.iastate.edu (USENET News System) Organization: Iowa State University, Ames IA References: <1992Sep1.094300.2414@nuscc.nus.sg> <SMITH.92Sep1154327@minerva.harvard.edu> <alex.715433129@pv3448.vincent.iastate.edu> <SMITH.92Sep2103757@minerva.harvard.edu> Date: Thu, 3 Sep 1992 12:57:15 GMT Lines: 20