Let be a symmetric matrix of order with the elements of the main diagonal equal to and those on the upper and lower codiagonals equal to . Let be a matrix of order , whose th column is defined as linearly spaced elements in , . Solve the systems . The -norm of the vector is, approximately:

Let be the matrix of order , generated by the command . Starting from the unitary vector, execute iterations of the inverse power method applied to . The absolute error associated to the approximation of the eigenvalue that is the closest to (take the value returned by eig as reference), is approximately:

Let be a tridiagonal matrix with order such that the diagonal elements are equal to , the upper diagonal elements are equal to and the lower diagonal elements are equal to . Build a vector , whose elements are equally spaced values in , and solve the linear system , using the SVD decomposition of . Within the steps of such method, let be the solution of the linear system with coefficient matrix ; the quantity is approximately: