Preconditioning Complex Symmetric Linear Systems

Figure 1

The polynomials described in Lemma 10: in the first row the product showing the approximation of the identity; in the second row the explicit graph of the polynomial preconditioner compared with the function ; in the third row the performance of the preconditioner in terms of the degree, condition number, and concentration of the eigenvalues of the coefficient matrix around 1. The left column represents the Jacobi weight and the right column the Chebyshev polynomials.