Parallel solution of saddle point systems with nested iterative solvers based on the Golub‐Kahan Bidiagonalization

Implicit-Factorization Preconditioning and Iterative Solvers for Regularized Saddle-Point Systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations...

On the parallel solution of dense saddle-point linear systems arising in stochastic programming

We present a novel approach for solving dense saddle-point linear systems in a distributedmemory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have many impo...

Fast Iterative Solution of Saddle Point Problems in Optimal Control Based on Wavelets

Generalized iterative methods for solving double saddle point problem

In this paper, we develop some stationary iterative schemes in block forms for solving double saddle point problem. To this end, we first generalize the Jacobi iterative method and study its convergence under certain condition. Moreover, using a relaxation parameter, the weighted version  of the Jacobi method together with its convergence analysis are considered. Furthermore, we extend a method...

The parallel solution of dense saddle-point linear systems arising in stochastic programming

We present a novel approach for solving dense saddle-point linear systems in a distributedmemory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have many impo...