The alternative-triangular method

Seidel method. As we have mentioned above, implicit schemes are rather stable in comparison with explicit ones. Seidel method, being the simplest implicit iterative one, is considered first. The object of investigation here is the system of linear algebraic equations 

Within these notations, Seidel method can be written as follows  

Further identification with the preceding canonical form reveals 

In such a setting it seems reasonable to begin operations at the node 

On account of the basic theorem proved in Section 1 of the present chapter Seidel method converges if the operator A is self-adjoint and positive. More specifically, the sufficient stability condition (11) for the convergence of iterations in scheme (3 ) with a non-self-adjoint operator B takes the form 

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