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Deriving the X-Z Identity from Auxiliary Space Method*

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Domain Decomposition Methods in Science and Engineering XIX

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 78))

Abstract

In this paper we discuss iterative methods to solve the linear operator equation

* The author is supported in part by NSF Grant DMS-0811272, and in part by NIH Grant P50GM76516 and R01GM75309. This work is also partially supported by the Beijing International Center for Mathematical Research.

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Bibliography

  1. D. Cho, J. Xu, and L. Zikatanov. New estimates for the rate of convergence of the method of subspace corrections. Numer. Math. Theor. Methods Appl., 1:44–56, 2008.

    MATH  MathSciNet  Google Scholar 

  2. M. Griebel and P. Oswald. On the abstract theory of additive and multiplicative Schwarz methods. Numer. Math., 70:163–180, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  3. S.V. Nepomnyaschikh. Decomposition and fictitious domains methods for elliptic boundary value problems. In Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Norfolk, VA, 1991), pp. 62–72, SIAM, Philadelphia, PA, 1992.

    Google Scholar 

  4. P.S. Vassilevski. Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations. Springer, New York, NY, 2008.

    Google Scholar 

  5. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev., 34:581–613, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Xu. The auxiliary space method and optimal multigrid preconditioning techniques for unstructured meshes. Computing, 56:215–235, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Xu and L. Zikatanov. The method of alternating projections and the method of subspace corrections in Hilbert space. J. Am. Math. Soc., 15:573–597, 2002.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Long Chen .

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Chen, L. (2011). Deriving the X-Z Identity from Auxiliary Space Method*. In: Huang, Y., Kornhuber, R., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11304-8_35

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