Adding Plotting to bisection method
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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;
回答（1 个）
Alan Stevens
2021-2-13
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
6 个评论
gracias claude
2021-2-13
gracias claude
2021-2-13
Alan Stevens
2021-2-13
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
2021-2-13
gracias claude
2021-2-13
Alan Stevens
2021-2-13
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')
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2021-2-13
2021-2-13
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