Adding Plotting to bisection method

Not sure what the c is in this bisection method. Also I would like to add plotting of the intervals

function [x,e] = MyBisectFunc(f, a1,b1, number)

format long

c1 = f(a1); d1 = f(b1);

if c1*d1 > 0.0

error ('Func has same sign at both endpoints')

end

for i = 1:number

x = (a1 + b1) /2;

y = f(x);

disp([x,y])

if y == 0.0

e = 0

break

end

if c*y < 0

b = x

else

a = x

end

end

x = (a1 + b1)/2;

e = (b1 - a1) /2;

Answer 1

[Alan Stevens]

Like so:

f = @(x) x^2 - 2;  % arbitrary function

a1 = 0; b1 = 1.8;  % initial end-points

c1 = f(a1); d1 = f(b1);
if c1*d1 > 0.0
error ('Func has same sign at both endpoints')
end

number = 20;
for i = 1:number
    
    c1 = f(a1); d1 = f(b1);
    if c1*d1 > 0.0
    error ('Func has same sign at both endpoints')
    end

    x = (a1 + b1) /2;
    y = f(x);
    disp([x,y])
    if abs(y) < 10^-8
       break
    end
    if c1*y < 0    %  c1 not c
        b1 = x;
    else
        a1 = x;
    end
    
end

[gracias claude]

What's this ?

`if abs(y) < 10^-8

break

end`

[gracias claude]

How do I plot the intervals ?

[Alan Stevens]

Never test for exact equality when dealing with floating point numbers, test for a small difference from the desired value.

For the intervals you could keep a record of the a1 and b1 values (by a1(i) = ...etc) then plot them against 1:number at the end.

[gracias claude]

so like

if ...

invervalX(i) = x;

end

else

intervalY(i) = x;

for i = 1:number

plot(intervalX(i), intervalY(i))

end;

[gracias claude]

not very familar with the syntax

[Alan Stevens]

This section

if abs(y) < 10^-8
       break
    end

breaks out of the loop if the condition is met. Probably best to remove it if you want to plot the intervals. You'll need to do something like:

f = @(x) x^2 - 2;  % arbitrary function

number = 20;  % number of iterations
lo = zeros(1,number);   % initialise vector
hi = zeros(1,number);
lo(1) = 0;
hi(1) = 1.8;
for i = 1:number-1
    
    flo = f(lo(i)); fhi = f(hi(i));
    if flo*fhi > 0.0
    error ('Func has same sign at both endpoints')
    end

    mid = (lo(i) + hi(i)) /2;
    fmid = f(mid);
   
    if flo*fmid < 0    %  c1 not c
        hi(i+1) = mid;
        lo(i+1) = lo(i);
    else
        lo(i+1) = mid;
        hi(i+1) = hi(i);
    end
    
end
disp([mid fmid])
plot(1:number,abs(hi-lo),'o'),grid
xlabel('iteration number'), ylabel('interval')