Abstract
We consider the SIMPLE preconditioning for block two‐by‐two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented. The relationship between the two different formulations spectrum of the SIMPLE preconditioned matrix is established by using the theory of matrix eigenvalue, and some corresponding results in recent article by Li and Vuik (2004) are extended.
Highlights
A BT x f1.1 y C −D y g where A ∈ Rn×n is nonsingular, B, C ∈ Rm×n m ≤ n , D ∈ Rm×m. Systems of the form 1.1 arise in a variety of scientific and engineering applications, such as linear elasticity, fluid dynamics, electromagnetics, and constrained quadratic programming 1–4
Consider the two-by-two generalized saddle point problems x A BT x f A≡1.1 y C −D y g where A ∈ Rn×n is nonsingular, B, C ∈ Rm×n m ≤ n, D ∈ Rm×m
Krylov subspace methods are considered as one kind of the important and efficient iterative techniques for solving the large sparse linear systems because these methods are cheap to be implemented and are able to fully exploit the sparsity of the coefficient matrix
Summary
1.1 y C −D y g where A ∈ Rn×n is nonsingular, B, C ∈ Rm×n m ≤ n , D ∈ Rm×m. Systems of the form 1.1 arise in a variety of scientific and engineering applications, such as linear elasticity, fluid dynamics, electromagnetics, and constrained quadratic programming 1–4. Krylov subspace methods are considered as one kind of the important and efficient iterative techniques for solving the large sparse linear systems because these methods are cheap to be implemented and are able to fully exploit the sparsity of the coefficient matrix Since the coefficient matrix of 1.1 is often extremely ill-conditioned and highly indefinite, the convergence speed of Krylov subspace methods can be unacceptably slow. Some corresponding results in 10 are extended to two-by-two generalized saddle point problems
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
