English: Arnoldi iteration demonstrating convergence of Ritz values (red) to the eigenvalues (black) of a 400x400 matrix, composed of uniform random values on the domain [-0.5 +0.5]. The small circle near the origin represents the arithmetic mean of the eigenvalues. The large circle is centered at this point and has a radius equivalent to the largest Euclidean distance, in the complex-plane, to an eigenvalue. Note that at each step of the Arnoldi iteration an additional Ritz value is added and the Ritz values (eigenvalues of the Hessenberg matrix computed at each Arnoldi iteration) converge to the extreme (outermost) eigenvalues first.