rendered paste bodyf = @(x) x.^5;
n = 5;
matrix = ones(5)
for i=0:n
tarray(i+1) = i/n;
end
for j=1:(n+1)
for i=1:(n+1)
matrix(j,i) = tarray(i).^(j-1);
end
end
matrixanswer = [0 0 0 0 0];
for i=1:(n+1)
matrixanswer(i) = f(tarray(i));
end
matrixanswer
matrixanswer = matrixanswer';
c = cond(matrix);
solution = matrix\matrixanswer;
residualvector = (matrix*solution) - matrixanswer;
fprintf('The Condition of the Row-Based N=5 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector
matrixanswer = [0 0 0 0 0];
for i=1:(n+1)
for j=1:(n+1)
matrix(i,j) = tarray(i).^(j-1);
end
end
for i=1:(n+1)
matrixanswer(i) = f(tarray(i));
end
matrixanswer = matrixanswer';
c = cond(matrix);
solution = matrix\matrixanswer;
residualvector = (matrix*solution) - matrixanswer;
fprintf('The Condition of the Column-Based N=5 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector
% The Condition of the Row-Based N=5 matrix is 4924.37106 and the solution is
%
% solution =
%
% -6.8503
% 37.8620
% -84.0653
% 93.6480
% -52.2980
% 11.7037
%
% And the Residual Vector is
%
% residualvector =
%
% 1.0e-014 *
%
% 0.1776
% 0.0320
% 0.1357
% -0.3927
% 0.0777
% 0.1776
%
% The Condition of the Column-Based N=5 matrix is 4924.37106 and the solution is
%
% solution =
%
% 0
% 0
% 0
% 0
% 0
% 1
%
% And the Residual Vector is
%
% residualvector =
%
% 0
% 0
% 0
% 0
% 0
% 0
f = @(x) x.^5;
n = 30;
matrix = ones(30)
matrixanswer = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
for i=0:n
tarray(i+1) = i/n;
end
for j=1:(n+1)
for i=1:(n+1)
matrix(j,i) = tarray(i).^(j-1);
end
end
for i=1:(n+1)
matrixanswer(i) = f(tarray(i));
end
matrixanswer;
matrixanswer = matrixanswer';
c = cond(matrix);
solution = matrix\matrixanswer;
residualvector = (matrix*solution) - matrixanswer;
fprintf('The Condition of the Row-Based N=30 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector
matrixanswer = [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
for i=1:(n+1)
for j=1:(n+1)
matrix(i,j) = tarray(i).^(j-1);
end
end
for i=1:(n+1)
matrixanswer(i) = f(tarray(i));
end
matrixanswer = matrixanswer';
c = cond(matrix);
solution = matrix\matrixanswer;
residualvector = (matrix*solution) - matrixanswer;
fprintf('The Condition of the Column-Based N = 30 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector
% The Condition of the Row-Based N=30 matrix is 2459531274782167600.00000 and the solution is
% solution =
% 1.0e+010 *
% -0.0000
% 0.0001
% -0.0006
% 0.0040
% -0.0198
% 0.0739
% -0.2194
% 0.5295
% -1.0558
% 1.7586
% -2.4620
% 2.9059
% -2.8912
% 2.4192
% -1.6980
% 1.0041
% -0.5167
% 0.2563
% -0.1431
% 0.0910
% -0.0558
% 0.0284
% -0.0109
% 0.0027
% -0.0002
% -0.0002
% 0.0001
% -0.0000
% 0.0000
% -0.0000
% 0.0000
% And the Residual Vector is
% residualvector =
% 1.0e-006 *
% 0.0123
% -0.0347
% -0.3498
% 0.7121
% 0.1050
% 0.0210
% -0.0416
% 0.0196
% 0.0092
% 0.0151
% 0.0095
% 0.0016
% -0.0010
% 0.0003
% 0.0002
% 0.0001
% 0.0000
% 0.0001
% 0.0001
% 0.0002
% 0.0001
% -0.0000
% -0.0000
% 0.0000
% 0.0000
% -0.0000
% 0.0000
% -0.0000
% 0.0000
% 0.0000
% 0.0000
% Warning: Matrix is close to singular or badly scaled.
% Results may be inaccurate. RCOND = 1.647133e-020.
% > In interpolate at 144
% The Condition of the Column-Based N = 30 matrix is 3381333759104609300.00000 and the solution is
% solution =
% 0
% 0.0000
% -0.0000
% 0.0000
% -0.0000
% 1.0000
% -0.0000
% 0.0000
% -0.0001
% 0.0004
% -0.0014
% 0.0040
% -0.0085
% 0.0124
% -0.0097
% -0.0036
% 0.0180
% -0.0142
% -0.0103
% 0.0256
% -0.0049
% -0.0301
% 0.0341
% -0.0054
% -0.0142
% 0.0049
% 0.0117
% -0.0146
% 0.0078
% -0.0021
% 0.0002
% And the Residual Vector is
% residualvector =
% 1.0e-015 *
% 0
% -0.0326
% -0.0595
% -0.0901
% -0.1109
% -0.1323
% -0.1501
% -0.1647
% -0.1778
% -0.1913
% -0.2047
% -0.2177
% -0.2220
% -0.2325
% -0.2429
% -0.2325
% -0.2429
% -0.2429
% -0.2776
% -0.2637
% -0.2498
% -0.1943
% -0.3331
% -0.3886
% -0.1665
% -0.2776
% -0.1110
% -0.1110
% -0.3331
% -0.3331
% -0.2220
%
%
%