MaplePrimes - answers and comments on Question, Rounding with Fsolve

assignment

acer — Thu, 07 Feb 2013 01:27:35 Z

You've forgotten the colon in := when trying to assign to `Rounding`.

restart;

ans:=fsolve(sin(x)=0, x=2..4);

                          3.141592654

evalf[5](ans);

                             3.1416

Rounding:=-infinity:

evalf[5](ans);

                             3.1415

acer

Oops

jschulzb — Thu, 07 Feb 2013 04:26:38 Z

Opps, sorry I blamed fsolve for this. But I'm still getting an error on what I'm trying.

I solve two equations for two unkowns,

soln:=fsolve({xp=X, yp=Y}, {t,theta}, t=(tn[n])..1000, theta=-Pi..Pi):

Then compute xp and X, xp and Y to double check and they give

xp= 0.7254021383

X= 0.7254021381

yp= -.7295245847

Y = -.7295245853

Shouldn't they be the same? Why is there so much error in them and how can I eliminate this? The forumlas for xp and X are

xp:= x[n] + mag[n]*(t-tn[n])*cos(alpha[n]+phi[n]):

X:= ( 1 + 0.2*sin(t)*sin(2*theta) ) * cos(theta) ;

Thanks,

The errors accrue in eval after fsolve returns

Carl Love — Thu, 07 Feb 2013 09:24:26 Z

The answers you got from fsolve are correct. The deviations accumulate because of round-off in the evaluation of xp, X, yp, and Y. That's just the nature of floating-point computations. The following example "tower" of computations at successively higher values of Digits shows that each answer returned by fsolve is correct to the requested number of digits, yet the "check" evaluation of the original equations is usually not accurate to that same number of digits.

p1,p2,p3,p4:= seq(randpoly([x,y]), k= 1..4):
for k from 3 to 15 by 2 do
   Digits:= k:
   soln:= fsolve({p1=p2, p3=p4}, {x,y});
   eval([p1,p2,p3,p4], soln)
od;

Digits := 3
soln := {x = .448, y = -.492}
[-1.1, -1.1, -.99, -.999]
Digits := 5
soln := {x = .44765, y = -.49237}
[-1.138, -1.138, -1.0135, -1.0134]
Digits := 7
soln := {x = .4476498, y = -.4923714}
[-1.13839, -1.13838, -1.013304, -1.013301]
Digits := 9
soln := {x = .447649842, y = -.492371448}
[-1.1383856, -1.1383856, -1.01330066, -1.01330067]
Digits := 11
soln := {x = .44764984210, y = -.49237144750}
[-1.138385629, -1.138385629, -1.0133006602, -1.0133006606]
Digits := 13
soln := {x = .4476498420985, y = -.4923714475019}
[-1.13838562902, -1.13838562902, -1.013300660590, -1.013300660592]
Digits := 15
soln := {x = .447649842098485, y = -.492371447501895}
[-1.1383856290149, -1.1383856290149, -1.01330066059060, -1.01330066059061]