Re: NSolve problem
- To: mathgroup at smc.vnet.net
- Subject: [mg27553] Re: [mg27541] NSolve problem
- From: BobHanlon at aol.com
- Date: Wed, 7 Mar 2001 04:07:49 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
poly[x_] :=
-379610373 +
86108525122 x -
9494410812843 x^2 +
678033800618890 x^3 -
35256637347077513 x^4 +
1422785868781829532 x^5 -
46379987523224586918 x^6 +
1255110040775305672800 x^7 -
28757943661703317295081 x^8 +
566216540434141788242036 x^9 -
9689635918166905495882851 x^10 +
145419622102662664506687100 x^11 -
1927635748101251322270468277 x^12 +
22698320261526730755198553574 x^13 -
238516616444064255358326013794 x^14 +
2244844544457248209076495840902 x^15 -
18977700242148569406030260324295 x^16 +
144425378677250071307785407099514 x^17 -
991008485501837267612722683739742 x^18 +
6137577944863948353668001351379085 x^19 -
34326439784958730341338590620522553 x^20 +
173372427244970231511243462159022530 x^21 -
790386259690389861011499411484727356 x^22 +
3249150512801263497674821800877444750 x^23 -
12025273387738045949766927419057733779 x^24 +
39983125143255083338516711567117321554 x^25 -
119092149085329990604796332906238009003 x^26 +
316623088476789267411001214031813664920 x^27 -
747964023676923486311300650584136934167 x^28 +
1561105298212051506376403179694366814908 x^29 -
2858356540987341736071315091852197268914 x^30 +
4550488627005201158356170201262005359426 x^31 -
6227602171254861022800069187941498698916 x^32 +
7219321171308545919834020175759542752800 x^33 -
6950806520792700621314978752272893634603 x^34 +
5408604513390527799203743488644413596831 x^35 -
3267975175700805824009526616434042764990 x^36 +
1438562129094179414396635651311443079894 x^37 -
410398690910611254706353259635396975000 x^38 +
56948086997945333979944420780869994640 x^39;
Plot[poly[x], {x, 0.07, 0.3}, Frame -> True, Axes -> False,
PlotRange -> {-0.2, 0.6}];
There is obviously a problem with precision
rpoly[x_] := poly[Rationalize[x, 10^-15]];
Plot[rpoly[x], {x, 0.07, 0.3}, PlotRange -> All, Frame -> True,
Axes -> False];
The polynomial appears to be an approximation of zero over an interval.
Trying to use NSolve is not apt to be fruitful.
Bob Hanlon
In a message dated 2001/3/3 4:10:47 AM, mtpagesj at lg.ehu.es writes:
>The following computation involving finding the roots of a fairly
>"large" polynomial produces these effects on an iMac and a G4 running
>version 4.0.1.0
>
>* The kernel quits inmediatly
>* The Finder announces a type 2 or type 3 error
>* The computer hangs when quitting the frontend or restarting
>
>Before finding this problem, I have succefully solved thousands of similar
>equations. It is only this particular polynomial that produces this
>behaviour.
>
>poly =
>-379610373 +
>86108525122 x -
>9494410812843 x^2 +
>678033800618890 x^3 -
>35256637347077513 x^4 +
>1422785868781829532 x^5 -
>46379987523224586918 x^6 +
>1255110040775305672800 x^7 -
>28757943661703317295081 x^8 +
>566216540434141788242036 x^9 -
>9689635918166905495882851 x^10 +
>145419622102662664506687100 x^11 -
>1927635748101251322270468277 x^12 +
>22698320261526730755198553574 x^13 -
>238516616444064255358326013794 x^14 +
>2244844544457248209076495840902 x^15 -
>18977700242148569406030260324295 x^16 +
>144425378677250071307785407099514 x^17 -
>991008485501837267612722683739742 x^18 +
>6137577944863948353668001351379085 x^19 -
>34326439784958730341338590620522553 x^20 +
>173372427244970231511243462159022530 x^21 -
>790386259690389861011499411484727356 x^22 +
>3249150512801263497674821800877444750 x^23 -
>12025273387738045949766927419057733779 x^24 +
>39983125143255083338516711567117321554 x^25 -
>119092149085329990604796332906238009003 x^26 +
>316623088476789267411001214031813664920 x^27 -
>747964023676923486311300650584136934167 x^28 +
>1561105298212051506376403179694366814908 x^29 -
>2858356540987341736071315091852197268914 x^30 +
>4550488627005201158356170201262005359426 x^31 -
>6227602171254861022800069187941498698916 x^32 +
>7219321171308545919834020175759542752800 x^33 -
>6950806520792700621314978752272893634603 x^34 +
>5408604513390527799203743488644413596831 x^35 -
>3267975175700805824009526616434042764990 x^36 +
>1438562129094179414396635651311443079894 x^37 -
>410398690910611254706353259635396975000 x^38 +
>56948086997945333979944420780869994640 x^39;
>
>NSolve[poly==0,x,100]
>