Block triangular preconditioners based on symmetric-triangular decomposition for generalized saddle point problems

摘要

In this paper, the symmetric-triangular decomposition is further studied to construct a class of block triangular preconditioners for generalized saddle point problems such that the preconditioned generalized saddle point matrices are symmetric and positive definite. Then the (preconditioned) conjugate gradient iterative method can be used. Three specific preconditioners are studied in detail. Eigen-properties of the corresponding preconditioned generalized saddle point matrices are studied. In particular, upper bounds on the condition number of the preconditioned matrices are analyzed. Finally, numerical experiments of a model Stokes equation are given to illustrate the efficiency of the new proposed preconditioners.