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Our class was tasked to develop programs for the Fixed Point Method, Newton-Rhapson Method, and the Secant Method, then create a subroutine that could compute the order of the rate of convergence for all the iterative methods. I DO know the orders of rate of convergence of each method, it's just that I can't demonstrate it in Scilab, the program we use in our class (although I also tried to demonstrate it in Matlab)

The Order can be derived from the formula

[itex]

e_{n+1} = C |e_{n}|^q

[/itex]

hence,

[itex]

q= {{\ln(e_{n+1}) - \ln(C) }\over \ln(e_n)}

[/itex]

What I've done so far is create 2 vectors containing iterates. One vector X contains the 1st, 2nd, ... nth iterate, while the other Y contains the 2nd, 3rd, ..., (n+1)th iterate. I then create a new vector E=Y-X which contains the errors in-between successive iterates. This is the part where I'm stuck - I have no clue as to how to compute for the asymptotic error constant (which is the only unknown I need to find q). I'm not even sure if the mathematical framework is correct... is there anything wrong with it?

All help is appreciated

reli~

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# Finding the order of the rate of convergence

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