Consider the fixed-point iteration xn+1 = 9(n). a) Under what conditions will it converge to the...

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Consider the fixed-point iteration xn+1 = 9(n). a) Under what conditions will it converge to the fixed point r, = 6(x.)? b) Sometimes when it diverges people try under-relaxation, which is to replace the above with xn+1 =ran + (1- r)(xn), where r is an adjustable relaxation factor. Show that if the original iteration diverges, then convergence can be restored with under-relaxation under certain circumstances. What are these circumstances? %3D Consider the fixed-point iteration xn+1 = 9(n). a) Under what conditions will it converge to the fixed point r, = 6(x.)? b) Sometimes when it diverges people try under-relaxation, which is to replace the above with xn+1 =ran + (1- r)(xn), where r is an adjustable relaxation factor. Show that if the original iteration diverges, then convergence can be restored with under-relaxation under certain circumstances. What are these circumstances? %3D