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Sufficient conditions for the convergent splittings of non-Hermitian positive definite matrices. (English) Zbl 0983.65044

In this very short paper (less than four pages) the authors present some sufficient conditions for the convergent splitting of non-Hermitian positive definite complex matrices. They demonstrate one interesting property of the Hermitian/skew-Hermitian splitting of positive definite complex matrices. The reported results may be used to identify the convergence of iterative methods for solving large sparse systems of linear equations.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
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References:

[1] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic Press: Academic Press New York · Zbl 0484.15016
[2] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.08602
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