Evaluation of ST preconditioners for saddle point problems

The general block ST decomposition of the saddle point problem is used as a preconditioner to transform the saddle point problem into an equivalent symmetric and positive definite system. Such a decomposition is called a block ST preconditioner. Two general block ST preconditioners are proposed for saddle point problems with symmetric and positive definite ( 1 , 1 ) -block. Some estimations of the condition number of the preconditioned system are given. The same study is done for singular ( 1 , 1 ) -block.

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