Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems. I: Theory. (English) Zbl 1078.65027

Block-diagonal preconditioners and the resulting preconditioned systems are introduced. Then the results of a study on the properties of the preconditioned matrices, in particular their eigendecompositions, are presented. The fixed point iteration and its related system are derived. The spectral radius of the fixed point iteration matrix and the spectrum of the related system matrix are also analyzed. Why it is more efficient to apply the GREMS algorithm to the related system than to the preconditioned system is explained. The paper concludes with results of numerical experiments and a discussion of scaling of nonlinear constraints in this constrained optimization problem to improve the convergence in each Newton step.


65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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