error running the code in while command in bisection method

umerfunction='x.^3';
x_lower=0;
x_upper=1;
   x_mid=(x_lower+x_upper)/2;
i=0;
while(abs(umerfunction(x_mid))>0.0001)
   
    fx=umerfunction(x_mid);
   X=[i,fx,x_upper,x_lower];
   disp X;
    if(umerfunction(x_mid)*umerfunction(x_upper))<0
        x_lower=x_mid;
    else x_upper=x_mid;
    end
    

ERROR:

Array indices must be positive integers or logical values.

Error in bisection (line 7)

while(abs(umerfunction(x_mid))>0.0001)

how to solve that issue? i m very frustated now regarding solving this.Thanks and honours in advance

Answer 1

[madhan ravi]

umerfunction=@(x)x.^3; 

Note: Also your loop is infinite loop since each time the condition will be satisfied either you need to add a break or change the condition.

[umer ansar]

thanks dear madhan. Your correction has recently solved my problem. but the loop ran infinitely as u pointed out. what can be the solution to make it adequntly finite?

note:i have checked from calculator that root is 3.57 so i have updated my lower and upper bounds to 3 and 4 respectively.i have been mentioned in my assignment question that the stopping criteria(accuracy of the root after which we should stop iterating) is 0.01.

thanks in advance and return

[madhan ravi]

Anytime :) , before going in depth the first line doesn't seem to work as you think though :

x_mid=(x_lower+x_upper)/2; =>  ( 0 + 1 ) / 2 => 0.5 , ( 0.5 ) ^ 3 => 0.125
or
( 3 + 4 ) / 2 => ( 3 + 4 ) / 2 => 3.5 , ( 3.5 ) ^ 3 =>    42.8750

so what do we observe from the above both the bounds that you try are always greater than 0.0001 , you need to rethink about your formula plus you don't seem to iterate x_mid over and over forever so basically the result becomes useless..