Numerical Linear Algebra with Applications

20.7.1 MATLAB Problems

20.16 Using the Jacobi and Gauss-Seidel methods, solve the system with tol = 0.5 × 10⁻¹⁴ and numiter = 50. In each case, print the number of iterations required and the relative residual ${\Vert b-Ax\Vert }_2/b$.

$\left[\begin{array}{cccc}6& -1& 2& 1\\ 1& 6& 1& -1\\ 0& 1& 3& 1\\ 1& -2& 1& 5\end{array}\right]\left[\begin{array}{c}3\\ 2\\ -6\\ 1\end{array}\right].$

20.17 This problem investigates convergence properties. The matrix $A=\left[\begin{array}{ccc}2& -1& 0\\ -1& 2& -1\\ 0& -1& 2\end{array}\right]$ is positive definite (Problem 20.10(b)).

a. Is matrix A strictly row diagonally dominant?

b. Is the Jacobi method ...