outputs result of bisection method to file

src/root_finding/bisection.m

@@ -1,35 +1,70 @@
-function root = bisection(xl,xu,epsilon, max_iterations, fx)
 
+% bisection method:
+%
+% Pors:
+% 1- Easy
+% 2- always converges
+% 3- the number of iterations required to attain an absolute error can be computer a priori.
+% 
+% Cons:
+% 1- Slower compared to other methods.
+% 2- Need to find inital guess Xl and Xu.
+% 3- No account is taken of the fact that if f(xl) is closer to zero, it's likely that root is 
+% closer to Xl.
+
+
+%
+% default value of epsilon = 0.00001
+% default value of max_iterations = 50
+%
+function root = bisection(xl, xu, epsilon, max_iterations, fx, output_file)
+ addpath('../'); % to use displaytable function
+ tic
  if(fx(xl)*fx(xu)>0)
  return;
  end
-
- root = implementation(xl, xu, xu, epsilon, max_iterations, fx, 0);
-
 
-end
+ [root, iterations, data] = implementation(xl, xu, xu, epsilon, max_iterations, fx, 0, []);
+ disp(iterations);
+ disp(data);
 
+ fileID = fopen(output_file,'w');
+ colheadings = {'Xr', 'Precision'};
+ rowheadings = {};
+ for i=1:iterations,
+ rowheadings{end+1} = int2str(i);
+ end
+
+ fms = {'.4f','.5E'};
+ wid = 16;
+ displaytable(data, colheadings, wid, fms, rowheadings, fileID, '|', '|');
 
-function root2 = implementation(xl, xu, xr_old, epsilon, max_iterations, fx, iterations)
+ timeElapsed = toc
+ fprintf(fileID, '\nnumber of iterations: %d\n', iterations);
+ fprintf(fileID, 'execution time: %f\n', timeElapsed);
+ fclose(fileID);
+end
 
- xr = (xl+xu)/2;
+
+function [root, iterations, data] = implementation(xl, xu, xr_old, epsilon, max_iterations, fx, iterations, data)
+ xr = (xl + xu) / 2;
 
  %01_STOP CONDITION*************************
- error=abs((xr-xr_old)/xr);
- iterations = iterations+1;
- if(error<=epsilon||iterations>max_iterations)
- root2 = xr;
+ approximate_relative_error = abs((xr - xr_old) / xr);
+ iterations = iterations + 1;
+ data = [data; xr, approximate_relative_error];
+ if(approximate_relative_error <= epsilon || iterations >= max_iterations)
+ root = xr;
  return;
  end
 
  %01_RECURSIVE STEP*************************
- if(fx(xr)*fx(xl)<0)
- root2 = implementation(xl, xr, xr, epsilon, max_iterations, fx, iterations);
+ if(fx(xr) * fx(xl) < 0)
+ [root, iterations, data] = implementation(xl, xr, xr, epsilon, max_iterations, fx, iterations, data);
  return;
  else
- root2 = implementation(xr, xu, xr, epsilon, max_iterations, fx, iterations);
+ [root, iterations, data] = implementation(xr, xu, xr, epsilon, max_iterations, fx, iterations, data);
  return;
  end
-
 
 end

src/root_finding/output.txt

@@ -0,0 +1,14 @@
+ | Xr| Precision|
+ 1| 0.0550| 1.00000E+00|
+ 2| 0.0825| 3.33333E-01|
+ 3| 0.0688| 2.00000E-01|
+ 4| 0.0619| 1.11111E-01|
+ 5| 0.0653| 5.26316E-02|
+ 6| 0.0636| 2.70270E-02|
+ 7| 0.0627| 1.36986E-02|
+ 8| 0.0623| 6.89655E-03|
+ 9| 0.0625| 3.43643E-03|
+10| 0.0624| 1.72117E-03|
+
+number of iterations: 10
+execution time: 0.065541

src/system_of_equations/lu_decomposition.m

@@ -7,7 +7,6 @@
  %solve for X
  solution=obtain_x_matrix(upper_matrix, y_matrix, num_of_unknowns);
 
-
 end
 
 
@@ -99,7 +98,3 @@
  system_matrix=result;
 
 end
-
-
-
-

src/system_of_equations/naive_gauss.m

@@ -7,8 +7,6 @@
  solutions=forward_elimination(system_matrix, num_of_unknowns);
  solutions=back_substitution(solutions, num_of_unknowns);
 
-
-
 end
 
 function new_system = forward_elimination(system_matrix, num_of_unknowns)