Re: critical points of a third order polynomial fit (simplification)

*To*: mathgroup at smc.vnet.net*Subject*: [mg68481] Re: [mg68466] critical points of a third order polynomial fit (simplification)*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Mon, 7 Aug 2006 01:40:44 -0400 (EDT)*References*: <200608060656.CAA23460@smc.vnet.net> <5951C758-2C5C-4727-AD67-41E11F62F79E@mimuw.edu.pl> <acbec1a40608060838n1c214499ledaa6ebdc94e0ebc@mail.gmail.com> <A35E92CF-D0AD-4DB3-8BCF-C23ECF0E51A4@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

Per offlist discussion with Andrzej Kozlowski, it is seen that Mathematica is capable of detecting the numerical ill conditioning in this problem when using arbitrary precision numbers. This can be tested by appending the following replacements to the definition of bracket: /. x_Real?InexactNumberQ :> SetPrecision[x, 14] /. x_Real?InexactNumberQ :> SetPrecision[x, 32]

**References**:**critical points of a third order polynomial fit (simplification)***From:*"Chris Chiasson" <chris@chiasson.name>