About improvement of the effectiveness of line-by-line recursive method for solving a difference elliptical equationsABOUT IMPROVEMENT OF THE EFFECTIVENESS OF LINE-BY-LINE RECURSIVE METHOD FOR SOLVING A DIFFERENCE ELLIPTICAL EQUATIONS.
L.N. Fomina
Kemerovo state university, Kemerovo
The article regards the technology to improve the effectiveness of line-by-line recursive method for solving a SLAE with the five-diagonal positive type matrixes by a combination of line-by-line recursive method and the biconjugate gradient stabilized method. It is shown that the traditional way by building a specialized preconditioner based on line-by-line recursive method to be partly valid to improve the effectiveness. The matter is that the traditional way improves the resolving possibilities which allows to build the solutions of a SLAE with matrixes characterized by condition numbers over 107-108 on the one hand, but on the other hand solving time of a system with other things being equal increases.
A new method allowing not only to solve much more rigid SLAE, but also to spend much less time to solve them is successfully developed by so-called direct combining of algorithms of line-by-line recursive method and the biconjugate gradient stabilized method. There is no need to use the preconditioner. The possibilities of this method are demonstrated by means of computing experiment. The superiority of new method both over initial line-by-line recursive method and over the most effective at present time biconjugate gradient stabilized method with preconditioner based on explicit Buleev method is shown.
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