Title: Preconditioning for Accurate Solutions of the Biharmonic Eigenvalue Problem

Abstract: Solving ill-conditioned systems poses two basic problems: convergence and accuracy. Preconditioning can overcome slow convergence, but this is only practical if the preconditioned system can be formed sufficiently accurately. In fact, for a fourth order operator, existing eigenvalue algorithms may compute smaller eigenvalues with little or no accuracy in standard double precision. In this talk, we combine standard matrix eigenvalue solvers with an accurate preconditioning scheme in order to compute the smallest eigenvalue of the biharmonic operator to machine precision in spite of ill-conditioning. The results on various domains are compared with the best known computations from the literature to demonstrate the accuracy and applicability of the method.