# Regula-falsi Method that keeps running

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BG on 19 Mar 2023
Commented: BG on 19 Mar 2023
I have this script for Regula-Falsi Method to get a root of a function but it just keeps running. Anyone can help find what's wrong?
f = @(x) 2.^x - x.^2 - 2; % Function whose roots are desired
xL = 4; xU = 5; % Initial guesses
Tol = 1e-6; % Tolerance (0.000001)
c = 0; % Counter for the no. of iterations
while abs( xU-xL ) > Tol
c = c + 1
xm = xU-f(xU)* (xU-xL)/f(xU)- f(xL); % Compute xm
fm = f(xm); % Evaluate the function at x = xm
% % Print the intermediate results
fprintf('Iteration: %d\t',c);
fprintf ('[xL,xU,xm ] = [%.6f, %.6f, %.6f]\n', xL,xU,xm);
if f(xL ) *fm < 0 % If the root is on the left,
xU = xm ; % then set xm as the new xU.
elseif fm * f( xU ) < 0 % But if the root is on the
xL = xm ; % then set xm as the new xL.
else
break; % Stop! xm is exactly the root
end
end
plot(xm,f(xm),'r*', 'Markersize', 10); % plot the xm points
fprintf ('The root is: %.6f \n', xm);

Alan Stevens on 19 Mar 2023
Brackets!!
f = @(x) 2.^x - x.^2 - 2; % Function whose roots are desired
xL = 4; xU = 5; % Initial guesses
Tol = 1e-6; % Tolerance (0.000001)
c = 0; % Counter for the no. of iterations
while abs( xU-xL ) > Tol
c = c + 1;
xm = xU-f(xU)* (xU-xL)/(f(xU)- f(xL)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Put brackets round f(xU)-f(xL)
fm = f(xm); % Evaluate the function at x = xm
% % Print the intermediate results
fprintf('Iteration: %d\t',c);
fprintf ('[xL,xU,xm ] = [%.6f, %.6f, %.6f]\n', xL,xU,xm);
if f(xL ) *fm < 0 % If the root is on the left,
xU = xm ; % then set xm as the new xU.
elseif fm * f( xU ) < 0 % But if the root is on the
xL = xm ; % then set xm as the new xL.
else
break; % Stop! xm is exactly the root
end
end
Iteration: 1
[xL,xU,xm ] = [4.000000, 5.000000, 4.285714]
Iteration: 2
[xL,xU,xm ] = [4.285714, 5.000000, 4.390866]
Iteration: 3
[xL,xU,xm ] = [4.390866, 5.000000, 4.425434]
Iteration: 4
[xL,xU,xm ] = [4.425434, 5.000000, 4.436351]
Iteration: 5
[xL,xU,xm ] = [4.436351, 5.000000, 4.439754]
Iteration: 6
[xL,xU,xm ] = [4.439754, 5.000000, 4.440811]
Iteration: 7
[xL,xU,xm ] = [4.440811, 5.000000, 4.441138]
Iteration: 8
[xL,xU,xm ] = [4.441138, 5.000000, 4.441240]
Iteration: 9
[xL,xU,xm ] = [4.441240, 5.000000, 4.441271]
Iteration: 10
[xL,xU,xm ] = [4.441271, 5.000000, 4.441281]
Iteration: 11
[xL,xU,xm ] = [4.441281, 5.000000, 4.441284]
Iteration: 12
[xL,xU,xm ] = [4.441284, 5.000000, 4.441285]
Iteration: 13
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 14
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 15
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 16
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 17
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 18
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 19
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 20
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 21
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 22
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 23
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 24
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 25
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 26
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 27
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 28
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 29
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
Iteration: 30
[xL,xU,xm ] = [4.441285, 5.000000, 4.441285]
plot(xm,f(xm),'r*', 'Markersize', 10); % plot the xm points fprintf ('The root is: %.6f \n', xm);
The root is: 4.441285
BG on 19 Mar 2023
Thank you so much. I didn't see that.

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