Question

I need help creating program for the Test_Bisection pseudocode. I need to find a root for each function f and g and get the output below.

Pseudocode Now let's construct pseudocode to carry out this procedure. We shall not try to create a piece of high-quality software with many "bells and whistles,” but we write the pseudocode in the form of a procedure for general use. This allows the reader an opportunity to review how a main program and one or more procedures can be connected. As a general rule, in programming routines to locate the roots of arbitrary functions, unnecessary evaluations of the function should be avoided because a given function may be costly to evaluate in terms of computer time. Thus, any value of the function that may be needed later should be stored rather than recomputed. A careless programming of the bisection method might violate this principle. The procedure to be constructed operates on an arbitrary function f. An interval [a, b] is also specified, and the number of steps to be taken, nmax, is given. Pseudocode to perform nmax steps of the bisection algorithm follows: procedure Bisection(f, a, b, nmax, E) integer n, nmax; real a, b, c, fa, fb, fc, error fa + f(a) fb + f(b) if sign(fa) = sign(fb) then output a, b, fa, fb output “function has same signs at a and b” return (Continued)

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

1)

clc%clears screen
clear all%clears history
close all%closes all files
format long
f = @(x) x^3-3*x+1;
e=1e-6;
a=0;
b=1;
iter = 0;
  
if f(a)*f(b)>=0

disp('No Root')

else

prev = (a+b)/2;
p=a;
while (abs(f(p))>e)
prev=p;

iter =iter+ 1;

p = (a+b)/2;

if f(p) == 0

break;

end

if f(a)*f(p)<0

b = p;

else

a = p;

end
fprintf('Iteration %d, root=%2.8f\n',iter,p);
if(iter==100)
disp('the required accuracy is not reached in 50 iterations');
end
end

end

- O X Pradeep do E C . Search Documentation EDITOR PUBLISH VIEW Insert E fx EH - D Comment % 92% & Breakpoints Run Indent 1 - EDIT Run Section El Advance 8 Run and Run and Advance Aduan Time BREAKPOINTS RUN O ох eulerSystem. m x ahk. m x nse_filt. m x + MATLAB R2018a HOME PLOTS APPS + G C Find Files 3 Compare - Go To - New Open Save Print Find FILE NAVIGATE hal Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m +1 saveee. mx bisectionmethodbypradeep.m x googleLinks. m x HomeworkLib2.m x testc. mx fprintf('Iteration fd, root=$2.8f\n', iter,p); if(iter==100) disp('the required accuracy is not reached in 50 iterations'); end end Workspace Name Value 0.3473 0.3473 1.0000e-06 49 - end Command Window New to MATLAB? See resources for Getting Started. Iteration 7, root=0.35156250 Iteration 8, root=0.34765625 Iteration 9, root=0.34570313 Iteration 10, root=0.34667969 Iteration 11, root=0.34716797 Iteration 12, root=0.34741211 Iteration 13, root=0.34729004 Iteration 14, root=0.34735107 Iteration 15, root=0.34732056 Iteration 16, root=0.34730530 Iteration 17, root=0.34729767 Iteration 18, root=0.34729385 Iteration 19, root=0.34729576 Iteration 20, root=0.34729671 fx >> We @(x}x^31x1 double) Hiter Ap prev 20 0.3473 0.3473 script Type here to search R Ln 49 col 4 dy ENG 3:30 PM IN 02/28/20 = a

2)

clc%clears screen
clear all%clears history
close all%closes all files
format long
f = @(x) x^3-2*sin(x);
e=1e-6;
a=0.5;
b=2;
iter = 0;
  
if f(a)*f(b)>=0

disp('No Root')

else

prev = (a+b)/2;
p=a;
while (abs(f(p))>e)
prev=p;

iter =iter+ 1;

p = (a+b)/2;

if f(p) == 0

break;

end

if f(a)*f(p)<0

b = p;

else

a = p;

end
fprintf('Iteration %d, root=%2.8f\n',iter,p);
if(iter==100)
disp('the required accuracy is not reached in 50 iterations');
end
end

end

- O X Pradeep do E C . Search Documentation EDITOR PUBLISH VIEW Insert E fx EH - D Comment % 92% & Breakpoints Run Indent 1 - EDIT Run Section El Advance 8 Run and Run and Advance Aduan Time BREAKPOINTS RUN O ох eulerSystem. m x ahk. m x nse_filt. m x + MATLAB R2018a HOME PLOTS APPS + G C Find Files 3 Compare - Go To - New Open Save Print Find FILE NAVIGATE hal Windows System32 Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details Editor - C:\Users\PRADEEP KALRA\Documents\MATLAB\saveee.m +1 saveee. mx bisectionmethodbypradeep.m x googleLinks. m x HomeworkLib2.m x testc. mx fprintf('Iteration fd, root=$2.8f\n', iter,p); if(iter==100) disp('the required accuracy is not reached in 50 iterations'); end end Workspace Name Value 1.2362 1.2362 1.0000e-06 @(x}x^3-2*sin(x) 49 - end Command Window New to MATLAB? See resources for Getting Started. Iteration 6, root=1.22656250 Iteration 7, root=1.23828125 Iteration 8, root=1.23242188 Iteration 9, root=1.23535156 Iteration 10, root=1.23681641 Iteration 1l, root=1.23608398 Iteration 12, root=1.23645020 Iteration 13, root=1.23626709 Iteration 14, root=1.23617554 Iteration 15, root=1.23622131 Iteration 16, root=1.23619843 Iteration 17, root=1.23618698 Iteration 18, root=1.23618126 Iteration 19, root=1.23618412 fx >> We Hiter Ap prev 1.2362 1.2362 script Ln 49 col 4 d x ENG 3:31 PM IN 02/28/20 = Type here to search A

Kindly revert for any queries

Thanks.