part3B_pr2.txt

diary on
format compact
type solve2_3b.m

function C = solve2_3b(A)
    size_of_A = size(A);
    n = size_of_A(1,1);
    format long, b = randi(10, n, 1)
    x1 = A\b;
    x2 = inv(A) * b;
    x3 = rref([A b]);
    x3 = x3(:,end);
    C = [x1 x2 x3];
    n1 = norm(minus(x1,x2));
    n2 = norm(minus(x2,x3));
    n3 = norm(minus(x3,x1)); 
    format long, N = [n1; n2; n3]
    format long, return
end
A = eye(4)
A =
     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1
solve2_3b(A)
b =
    10
     1
     5
     2
N =
     0
     0
     0
ans =
    10    10    10
     1     1     1
     5     5     5
     2     2     2
A = [4 0 -3 -7; -6 9 9 9; 7 -5 10 19; -1 2 4 -1]
A =
     4     0    -3    -7
    -6     9     9     9
     7    -5    10    19
    -1     2     4    -1
solve2_3b(A)
b =
    10
     1
     8
     9
N =
   1.0e-04 *
   0.000000000012864
   0.107253201187546
   0.107253201189822
ans =
   1.879740518962075   1.879740518962076   1.879746835443038
   0.486027944111777   0.486027944111776   0.486033519553073
   2.157185628742514   2.157185628742514   2.157181571815718
  -1.278942115768463  -1.278942115768462  -1.278947368421053 
format rat, A = hilb(4)
A =
       1              1/2            1/3            1/4     
       1/2            1/3            1/4            1/5     
       1/3            1/4            1/5            1/6     
       1/4            1/5            1/6            1/7     
solve2_3b(A)
b =
     9
     1
     4
     3
N =
   1.0e-08 *
   0.026824777352476
   0.108502270630065
   0.135298640136395
ans =
   1.0e+04 *
   0.056399999999997   0.056399999999997   0.056400000000000
  -0.563999999999958  -0.563999999999966  -0.564000000000000
   1.277999999999893   1.277999999999915   1.278000000000000
  -0.797999999999929  -0.797999999999942  -0.798000000000000
format rat, A = hilb(9)
A =
  Columns 1 through 4
       1              1/2            1/3            1/4     
       1/2            1/3            1/4            1/5     
       1/3            1/4            1/5            1/6     
       1/4            1/5            1/6            1/7     
       1/5            1/6            1/7            1/8     
       1/6            1/7            1/8            1/9     
       1/7            1/8            1/9            1/10    
       1/8            1/9            1/10           1/11    
       1/9            1/10           1/11           1/12    
  Columns 5 through 8
       1/5            1/6            1/7            1/8     
       1/6            1/7            1/8            1/9     
       1/7            1/8            1/9            1/10    
       1/8            1/9            1/10           1/11    
       1/9            1/10           1/11           1/12    
       1/10           1/11           1/12           1/13    
       1/11           1/12           1/13           1/14    
       1/12           1/13           1/14           1/15    
       1/13           1/14           1/15           1/16    
  Column 9
       1/9     
       1/10    
       1/11    
       1/12    
       1/13    
       1/14    
       1/15    
       1/16    
       1/17    
solve2_3b(A)
b =
     9
     5
    10
     2
     3
     2
     2
     9
     6
N =
   1.0e+06 *
   0.936494341184876
   0.898756566857970
   1.835247069862893
ans =
   1.0e+11 *
  -0.000044769736468  -0.000044769819727  -0.000044769900000
   0.003247289674963   0.003247295469302   0.003247301080000
  -0.056965195354481  -0.056965294082565  -0.056965389170000
   0.417857453320942   0.417858161017986   0.417858840890000
  -1.565823613786031  -1.565826221792047  -1.565828714810000
   3.253017755085654   3.253023069413168   3.253028189620000
  -3.789873542187753  -3.789879676017399  -3.789885543930000
   2.316924449955657   2.316928146955028   2.316931708410000
  -0.578383138780138  -0.578384064040321  -0.578384934110000
% Since hilb is poorly conditioned it's very sensitive to round-off errors, 
% ecspecially as the matrix size grows.
det(hilb(9))
ans =
     9.720278969918640e-43
diary off