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http://dx.doi.org/10.14317/jami.2020.175

SPECTRAL ANALYSIS OF THE MGSS PRECONDITIONER FOR SINGULAR SADDLE POINT PROBLEMS  

RAHIMIAN, MARYAM (Faculty of Mathematical Sciences, University of Guilan)
SALKUYEH, DAVOD KHOJASTEH (Faculty of Mathematical Sciences, University of Guilan)
Publication Information
Journal of applied mathematics & informatics / v.38, no.1_2, 2020 , pp. 175-187 More about this Journal
Abstract
Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.
Keywords
Saddle point problem; Singular; preconditioner; eigenvalue; symmetric positive definite; bound;
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