Which of the following fixed point iterations n+1 = g(n) will converge. Comment about their rate...

 

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Which of the following fixed point iterations n+1 = g(n) will converge. Comment about their rate of convergence based on g'(a). You can get rough idea of what a is within a few iterations. (a) n+1 = cos n starting with zo = 1 (b) In+1 = 1 + (n - 2)2 starting with ro = 1.38 (in this case a also is approximately 1.38) (c) *n+1 = 2an starting with zo = 0.5 (d) n+1 = sinn staring with ro = 1 - Which of the following fixed point iterations n+1 = g(n) will converge. Comment about their rate of convergence based on g'(a). You can get rough idea of what a is within a few iterations. (a) n+1 = cos n starting with zo = 1 (b) In+1 = 1 + (n - 2)2 starting with ro = 1.38 (in this case a also is approximately 1.38) (c) *n+1 = 2an starting with zo = 0.5 (d) n+1 = sinn staring with ro = 1 -

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In the context of iterative methods for solving equations the fixedpoint iteration is a numerical technique to find an approximation to a root of the ... View the full answer