Session D. Approximation methods in numerical linear algebra (ill-conditioned systems, matrix functions, ...). Organizers: C. Brezinski (Lille, F) and M. Eiermann (Freiberg, D) C. Brezinski, G. Rodriguez, and S. Seatzu Error estimates for choosing the best parameter in Tikhonov regularization A. Chesnokov, K. Deckers, and M. Van Barel A numerical solution of the constrained weighted energy problem P. G. Constantine and D. F. Gleich Spectral Methods for Parameterized Matrix Equations V. Druskin and M. Zaslavsky On convergence of Krylov subspace approximations of time-invariant dynamical systems O. G. Ernst Deflated Restarting of Krylov Subspace Approximations for Matrix Functions A. Frommer Verified Computation of Square Roots of a Matrix S. Güttel On the convergence of rational Krylov approximations to matrix functions U. Hämarik, R. Palm, and Toomas Raus On solution of linear problems by the extrapolated Tikhonov method V. Druskin, L. Knizhnerman, and M. Zaslavsky Shift optimization for solution of large scale evolutionary problems by means of Galerkin approach on rational Krylov subspaces P. Mathé Approximation theoretic aspects of variable Hilbert scales P. Novati Implementation of Lawson-Adams multistep methods for large stiff problems G. Rodriguez Matrix computations in the numerical solution of the nonlinear Schrödinger equation F. Sgallari Edge-preserving multilevel methods for deblurring, denoising, and segmentation