Problems "GSL"

  1. Using GSL special functions and gnuplot plot the Airy functions Ai(x) and Bi(x) (for a reasonable interval of x).
  2. Consider the following system of linear equations in the matrix form, 
    

    
[ 6.13  -2.90  5.86 ]
 [x0]   [6.23]

    

    
[ 8.08  -6.31  -3.89 ]
 [x1]  =  [5.37]

    

    
[ -4.36  1.00  0.19 ]
 [x2]   [2.29]

    1. Solve it using GSL.

      Hint: you can solve linear systems using one of the many methods, for example,

      • Householder solver for linear systems, 
        gsl_linalg_HH_solve
      • LU-decomposition, 
        gsl_linalg_LU_decomp
gsl_linalg_LU_solve
      • QR-decomposition, 
        gsl_linalg_QR_decomp
gsl_linalg_QR_solve
        See also:

        GSL manual → Linear Algebra → Householder solver for linear systems;
        GSL manual → Linear Algebra → LU Decomposition;
        GSL manual → Linear Algebra → QR Decomposition;
        GSL manual → Linear Algebra → Linear Algebra Examples.

    2. Check that you have the correct solution by multiplying the original matrix and the solution and comparing with the right-hand-side.
  3. (Optional) Compute the eigenvalues and eigenvectors of 4-th order Hilbert matrix, Hij = 1/(i + j + 1).