GPY

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These are questions asked by GPY

The algorithm that I need to replicate is as follows:

real function f(x,y)

integer n; real a,b,c,x,y

f<-max(|x|,|y|)

a<-min(|x|,|y|)

for n=1 to 3 do

b<-(a/f)^2

c<-b/(4+b)

f<-f+2*c*f

a<-ca

end for

end function f

How can I define f,a as  functions that I am later using as variables(in f=f+2cf,b=(a/f)^2)? also, is n just a variable for iteration? 

 

I've got a function f(x_n) = (x_n-1)^3

and need to show that for the iterative method

x_(n+1)= x_n - f(x_n)/(sqrt(f'(x_n)^2-f(x_n)*f''(x_n), at a simple root we have cubic convergence while at a multiple root, it converges linearly.

I understand that the approach is to write either a recursive function or a sequence, but i'm confused about the structure since both x and n are being incremented

 

I need to show what happens to the zero r=20 of f(x)= (x-1)(x-2)..(x-20)-(1/10^8)*(x^19) and the hint given is that the secant method in double precision gives an approximate in [20,21].

At present, I'm calling the secant method on f with a tolerance of 1/(10^12) with an initial x=20, but I'm stuck as to what the second initial value would be. What is the right approach to this question?

 

I've plotted the graph for this max function. Is there any way I can find the points of discontinuity in general and then use that to compute the derivatives at points where it exists?

I'm trying to get the RHL of exp1:=(2/(1+e^(-1/x)) as x->0+

and have l2:=limit(exp1,x=0,right) but that isn't giving me a value. How do I correct this? 

 

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