A class of new extended generalized shift-splitting preconditioners for \(3\times 3\) block saddle point problems

This paper introduces a class of new extended generalized shift-splitting (NEGSS) preconditioners for solving the \(3\times 3\) $3\times 3$ block saddle point problems (SPPs). The algorithm implementation of the NEGSS preconditioner, the convergence of the NEGSS iteration method and the eigenvalue distribution of the corresponding preconditioned matrix with parameter t are investigated. Numerical experiments demonstrate the effectiveness of the proposed method and verify our theoretical results.