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fixed_point.m

+% clc
+% clear all
+disp('Fixed Point method to a find root of f(x)=0 when the initial guess is given');
+%input  Note: Convert f(x)=0 interms of x=g(x)
+g1 = input('Enter the function g(x): ','s'); 
+g = inline(g1);
+x(1) = input('Enter the initial approximation/guess such that |g`(x)|<1 = ');
+
+max_itr = input('Enter the maximum no. of iterations = ');
+tol = input('Enter the tolerance = ');
+ 
+% Fixed Point method main program
+
+fprintf(' x(1)= %f\n', x(1));   % print the initial 'value
+for i=1:max_itr-1 % Note: repeat until max_itr starting 
+    %with zero
+    
+     x(i+1)= g(x(i));
+      
+     % print the approximate value in each iteration
+     fprintf(' x(%d)= %f\n',i+1, x(i+1));
+    
+     err= x(i+1)-x(i);
+     
+   if(abs(err)<=tol)
+     %ouput for the required tolerence
+     fprintf('The  approximate root after %d iterations is%f',i+1, x(i+1));
+     break;
+   end
+end
+
+if(abs(err)>tol)
+      %output when the given iterations are not sufficient
+   fprintf('Insufficient no. of iterations');
+end
+
+% ------------------------------------------------------------------------------ 
+% OUTPUT 1
+% Fixed Point method to a find root of f(x)=0 when the initial guess is given
+% Enter the function g(x): 1/(x^2+1)
+% Enter the initial approximation/guess such that |g`(x)|<1 = 
+%0.5
+% Enter the maximum no. of iterations = 5
+% Enter the tolerance = .1
+%  x(1)= 0.500000
+%  x(2)= 0.800000
+%  x(3)= 0.609756
+%  x(4)= 0.728968
+%  x(5)= 0.653000
+% The  approximate root after 5 iterations is 0.653000>>  
+% ------------------------------------------------------------------------------
+% OUTPUT 2
+% Enter the function g(x): 1/(x^2+1)
+% Enter the initial approximation/guess such that |g`(x)|<1 = 0.5
+% Enter the maximum no. of iterations = 5
+% Enter the tolerance = .01
+%  x(1)= 0.500000
+%  x(2)= 0.800000
+%  x(3)= 0.609756
+%  x(4)= 0.728968
+%  x(5)= 0.653000
+% Insufficient no. of iterations>> 
+% ------------------------------------------------------------------------------
+% OUTPUT 3
+% Fixed Point method to a find root of f(x)=0 when the initial guess is given
+% Enter the function g(x): 1/(x^2+1)
+% Enter the initial approximation/guess such that |g`(x)|<1 = 0.5
+% Enter the maximum no. of iterations = 20
+% Enter the tolerance = .01
+%  x(1)= 0.500000
+%  x(2)= 0.800000
+%  x(3)= 0.609756
+%  x(4)= 0.728968
+%  x(5)= 0.653000
+%  x(6)= 0.701061
+%  x(7)= 0.670472
+%  x(8)= 0.689878
+%  x(9)= 0.677538
+%  x(10)= 0.685374
+% The  approximate root after 10 iterations is 0.685374>> 
+% 
+% ------------------------------------------------------------------------------
+% OUTPUT 3
+% Fixed Point method to a find root of f(x)=0 when the initial guess is given
+% Enter the function g(x): 1/(x^2+1)
+% Enter the initial approximation/guess such that |g`(x)|<1 = 0.5
+% Enter the maximum no. of iterations = 20
+% Enter the tolerance = .00001
+%  x(1)= 0.500000
+%  x(2)= 0.800000
+%  x(3)= 0.609756
+%  x(4)= 0.728968
+%  x(5)= 0.653000
+%  x(6)= 0.701061
+%  x(7)= 0.670472
+%  x(8)= 0.689878
+%  x(9)= 0.677538
+%  x(10)= 0.685374
+%  x(11)= 0.680394
+%  x(12)= 0.683557
+%  x(13)= 0.681547
+%  x(14)= 0.682824
+%  x(15)= 0.682013
+%  x(16)= 0.682528
+%  x(17)= 0.682201
+%  x(18)= 0.682409
+%  x(19)= 0.682276
+%  x(20)= 0.682360
+% Insufficient no. of iterations>> 
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