Matlab Engineering math The Hilbert matrix is a special n ti

Matlab, Engineering math

The Hilbert matrix is a special n times n matrix whose (i, j)th entry is given by H_i, j = 1/(I + j - 1) The Hilbert matrix becomes very poorly conditioned even for moderate values of n. For each n = 1, 2, 3, ..., 12 create the n times n Hilbert matrix H using the MATLAB command hilb (type help hilb to get information about the function). Create an exact solution x consisting of a column vector of n ones. Then create a right hand side b = Hx in MATLAB. Now solve Hx_c = b in MATLAB using the \\ command so that xc = H\\b Generally xc will not be exactly x due to rounding error. Compute the infinity norm of the error using the MATLAB function norm as follows: Err(n) = norm(x - xc, inf) and hence the relative error. Compute the condition number of H for each n using the MATLAB cond function. Print a nicely formatted table with three columns: n, the condition number, and the relative error in the solution. For n = 6 and 10 display the full solutions (ie all n entries in the vector x_c) to see how accurate are the solutions.

Solution

warning(\'off\')
fprintf(\"n-Order \\t \\t RelativeError \\t \\t condOfH\ \")
fprintf(\"==================================================================\ \")
for n=0:12
    % Hilbert Matrix with nxn
    H = hilb(n) ;
   
    % xc = H * b
    % Create b with nx1
   
    b = ones(n,1) ;
   
    xc = H \\ b ;
   
    Err = norm(xc-b,Inf) ;
   
    condOfH = cond(H) ;
   
    fprintf(\"%8.8f \\t \\t %8.8f \\t \\t %8.8f \ \",n,Err,condOfH);

end
fprintf(\"==================================================================\ \");