Question

write the convergence criterion for fixed point interation method.
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Answer 1

Answer:

g(x) and g'(x) are continuous on an interval J about their root s of the equation x = g(x), and if |g'(x)|<1 for all x in the interval J then the fixed point iterative process xi+1=g( xi), i = 0, 1, 2, . . ., will converge to the root x = s for any initial approximation x0 belongs to the interval J .

Answer 2

Answer:

If g(x) and g'(x) are continuous on an interval J about their root s of the equation x = g(x), and if |g'(x)|<1 for all x in the interval J then the fixed point iterative process xi+1=g( xi), i = 0, 1, 2, . . ., will converge to the root x = s for any initial approximation x0 belongs to the interval J