MaplePrimes - answers and comments on Question, Programming

Bisection

tatan2501 — Wed, 18 Feb 2009 00:49:19 Z

I wrote the following code in maple.

a and b are the initial points. (a left, b right)

f is the function.

epsilon is the Maximum permissible error.

Good Luck

signum

acer — Wed, 18 Feb 2009 01:25:11 Z

You probably intended to get the functionality of signum instead of sign.

I'm referring to your code line,

while sign(f(b)) <> sign(f(c)) do

You might want to look at the respective help-pages ?signum and ?sign.

acer

recursive vs bisection

Jabz — Mon, 04 Jan 2010 19:05:46 Z

What's the difference between a recursive bisection method and the following code???

Bi_section:=proc(A,B,N,f)
local a,b,c,s,Err:
a:=A:
b:=B:
s:=evalf[1](10^(-N)):
if a >= b then
      printf("Incorrect Values %a",[a,b]);
else
   if sign(f(a)) = sign(f(b)) then
       printf("No Roots In The Interval %a",[a,b]);
else
    Err:=s+1:
           while Err>s do
               c:=evalf((a+b)/2):
                #print('f'(c)=f(c)):
               if sign(f(a)) * sign(f(c)) < 0 then
                      a:=a:
                      b:=c:
                      Err:=(abs(f(c))):
                   elif sign(f(c))* sign(f(b)) < 0 then
                      a:=c:
                      b:=b:
                      Err:=(abs(f(c))):

                   if f(c)=0                     then
                      Err:=0:
                 fi:
               fi:
          end do:
         fi:
        fi:
           printf("A solution to the function %a is %f to 6 dp",f(x),evalf(c)):
end proc:

Is this method not recursive???

Hi

Jabz — Wed, 18 Feb 2009 06:24:30 Z

"while sign(f(b)) <> sign(f(c)) do"

This line was suppose to mean that `do the iterations until both signs are equal`

I am having trouble with the continuity of the program. It only works out (a+b)/2 once and then stops or goes to infinite loops.

Hi

Jabz — Wed, 18 Feb 2009 06:15:13 Z

Thank so very much 4 ur help but am afraid ur code didnt work on the version of maple that am using. When i inputed ur code an error came up. This error is very similar to the error that i get. Here take a look:

Bisection:=proc(a,b,f,epsilon)
     local A,B,c,err:
     A:=a:
     B:=b:
     err:=epsilon+1:
     while err>epsilon do:
           c:=(A+B)/2:
           if evalf(eval(f,x=A)*eval(f,x=c))<o then
                 B:=c:
                 err:evalf(abs(eval(f,x=c))):
            else
                 if evalf(eval(f,x=B)*eval(f,x=c))<0 then
                   A:=c:
                   err:evalf(abs(eval(f,x=c))):
                  else
                  if eval(f,x=c)=0 then
                         err:=0:
                       end if:
                 end if:
            end if:
        end do:
        return evalf(c):
end proc:
Bisection(2,3,x^3-x-8,0.0001);
Error, (in Bisection) cannot determine if this expression is true or false: -10.25000000 < o

0 not o

tatan2501 — Wed, 18 Feb 2009 06:24:18 Z

In the fisrt if you wrote <o. (change o by 0).