how to control the accuracy of fzero
in [Matlab]
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From: Alan Weiss on 24 Jun 2010 08:15 I ask again: If you perturb the resulting solution x by executing x+eps(x) and x-eps(x), do you get better answers? On 6/23/2010 1:46 PM, Yu Li wrote: > Hi, > Thank you for your repaly. I did try fzero. The results are not > satifactory because the terms in the function are pretty small, in the > order of e-13. When I check the function values, some of them is only > e-14. The smallest one is e-17. I feel a zero should be at least in the > order of e-17. Thanks again. > > Yu > > Alan Weiss <aweiss(a)mathworks.com> wrote in message > <hvtgc6$ji$1(a)fred.mathworks.com>... >> >> Have you tried using fzero on your problem? >> If not, please do, and see if the results are satisfactory. >> If so, in what way were the results unsatisfactory? If you perturb the >> resulting solution x by executing x+eps(x) and x-eps(x), do you get >> better answers? >> >> You could also try scaling your problem so the terms are not so small. >> >> Alan Weiss >> MATLAB mathematical toolbox documentation
From: Steven Lord on 24 Jun 2010 10:41 "someone" <someone(a)somewhere.net> wrote in message news:hvueav$b39$1(a)fred.mathworks.com... > "Yu Li" <yuliyy(a)gmail.com> wrote in message > <hvtcn4$17s$1(a)fred.mathworks.com>... >> Hi, >> >> I need to solve an equation. each term is rather small, say, about >> 1e-13. I want the fzero solver to stop till the value of the function is >> smaller than 1e-19. I figure fzero don't take TolFun. Is there anything >> else I can do? Or I have to use another solver? Thank you very much. >> >> Best >> Yu > > Are you sure about fzero not taking the TolFun? > According to the documentation, fzero uses the optmiset structure which > uses TolFun. That's correct, FZERO can _accept_ an options structure returned from OPTIMSET that includes the TolFun parameter. That doesn't mean that FZERO _uses_ that option from the options structure. > Or. look at the TolX parameter in the options for fzero. http://www.mathworks.com/access/helpdesk/help/techdoc/ref/fzero.html There's a table listing the five options that FZERO uses from the options structure: Display, FunValCheck, OutputFcn, PlotFcns, and TolX. TolFun is not listed in that table. -- Steve Lord slord(a)mathworks.com comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ To contact Technical Support use the Contact Us link on http://www.mathworks.com
From: Yu Li on 24 Jun 2010 12:52 Hi, I checked. I got the same answer for x, x+eps(x) and x-eps(x). what does it mean then? Thanks a lot. Best Yu Alan Weiss <aweiss(a)mathworks.com> wrote in message <hvvi8g$l8n$2(a)fred.mathworks.com>... > I ask again: If you perturb the resulting solution x by executing > x+eps(x) and x-eps(x), do you get better answers? > > On 6/23/2010 1:46 PM, Yu Li wrote: > > Hi, > > Thank you for your repaly. I did try fzero. The results are not > > satifactory because the terms in the function are pretty small, in the > > order of e-13. When I check the function values, some of them is only > > e-14. The smallest one is e-17. I feel a zero should be at least in the > > order of e-17. Thanks again. > > > > Yu > > > > Alan Weiss <aweiss(a)mathworks.com> wrote in message > > <hvtgc6$ji$1(a)fred.mathworks.com>... > >> > >> Have you tried using fzero on your problem? > >> If not, please do, and see if the results are satisfactory. > >> If so, in what way were the results unsatisfactory? If you perturb the > >> resulting solution x by executing x+eps(x) and x-eps(x), do you get > >> better answers? > >> > >> You could also try scaling your problem so the terms are not so small. > >> > >> Alan Weiss > >> MATLAB mathematical toolbox documentation
From: Alan Weiss on 25 Jun 2010 09:44 fzero looks for a change of sign. You cannot always find a true zero because of various issues involved in floating-point arithmetic. If your initial solution x = fzero(yourFunction,x0) is not sufficiently accurate, you can 1. Create an option structure with a smaller value of TolX: opts = optimset('TolX',2*eps(x)); 2. Solve the problem again using the options structure x2 = fzero(yourFunction,x,opts); I think you would do better to scale your problem so the parameters are not so small, but the procedure I just described might work. You might be running into issues of round-off error or other numerical problems with your unscaled problem. Alan Weiss MATLAB mathematical toolbox documentation On 6/24/2010 12:52 PM, Yu Li wrote: > Hi, > > I checked. I got the same answer for x, x+eps(x) and x-eps(x). what does > it mean then? Thanks a lot. > > Best > Yu > > Alan Weiss <aweiss(a)mathworks.com> wrote in message > <hvvi8g$l8n$2(a)fred.mathworks.com>... >> I ask again: If you perturb the resulting solution x by executing >> x+eps(x) and x-eps(x), do you get better answers? >> >> On 6/23/2010 1:46 PM, Yu Li wrote: >> > Hi, >> > Thank you for your repaly. I did try fzero. The results are not >> > satifactory because the terms in the function are pretty small, in the >> > order of e-13. When I check the function values, some of them is only >> > e-14. The smallest one is e-17. I feel a zero should be at least in the >> > order of e-17. Thanks again. >> > >> > Yu >> > >> > Alan Weiss <aweiss(a)mathworks.com> wrote in message >> > <hvtgc6$ji$1(a)fred.mathworks.com>... >> >> >> >> Have you tried using fzero on your problem? >> >> If not, please do, and see if the results are satisfactory. >> >> If so, in what way were the results unsatisfactory? If you perturb the >> >> resulting solution x by executing x+eps(x) and x-eps(x), do you get >> >> better answers? >> >> >> >> You could also try scaling your problem so the terms are not so small. >> >> >> >> Alan Weiss >> >> MATLAB mathematical toolbox documentation
From: Yu Li on 25 Jun 2010 11:33 Hi, Thank you very much for explaining this. What you said is really helpful. I will try what you suggested. If you have time, giving some suggestions about how to scale the problem will be terrific. I have no idea how to do that. Thanks again. Best Yu Alan Weiss <aweiss(a)mathworks.com> wrote in message <i02brb$do2$1(a)fred.mathworks.com>... > fzero looks for a change of sign. You cannot always find a true zero > because of various issues involved in floating-point arithmetic. > > If your initial solution x = fzero(yourFunction,x0) is not sufficiently > accurate, you can > 1. Create an option structure with a smaller value of TolX: > opts = optimset('TolX',2*eps(x)); > 2. Solve the problem again using the options structure > x2 = fzero(yourFunction,x,opts); > > I think you would do better to scale your problem so the parameters are > not so small, but the procedure I just described might work. You might > be running into issues of round-off error or other numerical problems > with your unscaled problem. > > Alan Weiss > MATLAB mathematical toolbox documentation > > On 6/24/2010 12:52 PM, Yu Li wrote: > > Hi, > > > > I checked. I got the same answer for x, x+eps(x) and x-eps(x). what does > > it mean then? Thanks a lot. > > > > Best > > Yu > > > > Alan Weiss <aweiss(a)mathworks.com> wrote in message > > <hvvi8g$l8n$2(a)fred.mathworks.com>... > >> I ask again: If you perturb the resulting solution x by executing > >> x+eps(x) and x-eps(x), do you get better answers? > >> > >> On 6/23/2010 1:46 PM, Yu Li wrote: > >> > Hi, > >> > Thank you for your repaly. I did try fzero. The results are not > >> > satifactory because the terms in the function are pretty small, in the > >> > order of e-13. When I check the function values, some of them is only > >> > e-14. The smallest one is e-17. I feel a zero should be at least in the > >> > order of e-17. Thanks again. > >> > > >> > Yu > >> > > >> > Alan Weiss <aweiss(a)mathworks.com> wrote in message > >> > <hvtgc6$ji$1(a)fred.mathworks.com>... > >> >> > >> >> Have you tried using fzero on your problem? > >> >> If not, please do, and see if the results are satisfactory. > >> >> If so, in what way were the results unsatisfactory? If you perturb the > >> >> resulting solution x by executing x+eps(x) and x-eps(x), do you get > >> >> better answers? > >> >> > >> >> You could also try scaling your problem so the terms are not so small. > >> >> > >> >> Alan Weiss > >> >> MATLAB mathematical toolbox documentation
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