We present some sufficient and necessary conditions for convergent splitting of a non-Hermitian indefinite matrix. Some sufficient conditions to determinate a matrix with a (strongly) dominant symmetric part for a class of boundary value problem are also obtained. These results are applicable to identify the convergence of iterative methods for solving large sparse systems of linear equations.
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Chen, J., Li, W. Equivalent Conditions for Convergence of Splittings of Non-Hermitian Indefinite Matrices. J Sci Comput 30, 117–130 (2007). https://doi.org/10.1007/s10915-005-9022-3
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DOI: https://doi.org/10.1007/s10915-005-9022-3