Geodesic
Convergence of skew-symmetric iterative methods
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 75-79

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We propose a new technique for investigating the convergence of triangular skew-symmetric and product triangular skew-symmetric iterative methods (introduced earlier by the first author) based on the notion of a field of values of a matrix. We obtain formulas connecting the field of values of the initial matrix, the matrix which determines the iterative method, and eigenvalues of the iterative matrix. We prove that the mentioned methods can converge even if the initial matrix is not dissipative.
Keywords: skew-symmetric iterative methods, field of values of a matrix, convergence of iterative methods. 
@article{IVM_2011_6_a8,
     author = {L. A. Krukier and B. L. Krukier},
     title = {Convergence of skew-symmetric iterative methods},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--79},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a8/}
}
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L. A. Krukier; B. L. Krukier. Convergence of skew-symmetric iterative methods. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 75-79. http://geodesic.mathdoc.fr/item/IVM_2011_6_a8/