Section 6 : Existence of Solutions and Convergence of Iterative
Methods [12]
Example
9 [9 ]Consider system
-------(61)
-------(62)
which
has a solution (1,1). The iterative method
-------(63)
-------(64)
is
not a contraction mapping near (1,1) and the iterations do not converge even
if we start from a value close to the solution. On the other hand, the
rearrangement
-------(65)
-------(66)
is
a contraction mapping and solution converges if the starting guess is close to
the solution.
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