Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:
Verification Methods of Generalized Eigenvalue Problems and its Applications,
Transactions of the Japan Society for Industrial and Applied Mathematics , Vol.9, No.3 (1999) pp.137-150 (Japanese).
We consider numerical verification methods to obtain the maximum absolute value of generalized eigenvalue problems. We present four kinds of methods and compare the performance in various situations as well as give evaluation of the advantage and disadvantage of these methods. All numerical results have been calculated by the interval arithmetic software for considering the rounding error occuring in the calculation. Finally, we will present an application to an eigenvalue problem appeared in some a priori error estimates for the finite element solution of the Stokes equations.
The publisher holds the copyright on this manuscript.