Preconditioned iterative methods and perturbation analysis for a class of saddle point problems

Abstract

Saddle point problems (SPPs) have gained significant attention due to their diverse applications in computational science and engineering domains. This underscores the need for their efficient and robust solution methods. However, round-off and truncation errors in existing numerical approaches restrict solutions to approximations, raising critical concerns about their accuracy, sensitivity and reliability. To overcome these challenges, this thesis introduces preconditioned iterative methods for solving SPPs efficiently and employs perturbation analysis to assess the sensitivity and stability of the computed solutions. We specifically focus on two types of SPPs: the generalized saddle point problem (GSPP) and the double saddle point problem (DSPP).