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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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.
M. Griebel and P. Oswald. On the abstract theory of additive and multiplicative Schwarz methods. Numer. Math., 70:163–180, 1995.
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.
P.S. Vassilevski. Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations. Springer, New York, NY, 2008.
J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev., 34:581–613, 1992.
J. Xu. The auxiliary space method and optimal multigrid preconditioning techniques for unstructured meshes. Computing, 56:215–235, 1996.
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.
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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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DOI: https://doi.org/10.1007/978-3-642-11304-8_35
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