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Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 45)

Abstract

Matrices of two-by-two block form with matrix blocks of equal order arise in various important applications, such as when solving complex-valued systems in real arithmetics, in linearized forms of the Cahn–Hilliard diffusive phase-field differential equation model and in constrained partial differential equations with distributed control. It is shown how an efficient preconditioner can be constructed which, under certain conditions, has a resulting spectral condition number of about 2. The preconditioner avoids the use of Schur complement matrices and needs only solutions with matrices that are linear combinations of the matrices appearing in each block row of the given matrix and for which often efficient preconditioners are already available.

Keywords

Two-by-two block-structured matrices Preconditioning Complex-valued system Cahn–Hilliard phase-field model Optimal control Distributed control 

Notes

Acknowledgements

This work was supported by the European Regional Development Fund in the IT4 Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070).

Discussions with Maya Neytcheva on implementation aspects of the method are gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.IT4 Innovations DepartmentInstitute of Geonics AS CROstravaCzech Republic
  2. 2.King Abdulaziz UniversityJeddahSaudi Arabia

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