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MathGroup Archive 2007

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Iteratively determing successive values from previous values....

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80369] Iteratively determing successive values from previous values....
  • From: ashesh <ashesh.cb at gmail.com>
  • Date: Mon, 20 Aug 2007 03:37:48 -0400 (EDT)

Hi,

Need one help in determining the next value of a function from the
previous values.

Example:

x(i+1) = x(i) + 1;

If one iterates to find x(5), we should get it as (x(1) + 4), as the
initial value is x(1), which is obtained

x2 = x1+1;
x3 = x2 + 1 = (x1+1) + 2 = x1 + 2
x4 = x3 + 1 = (x2+1) + 1 = x2 + 2 = (x1+1) + 2 = x1 + 3
x5 = x4 + 1 = (x3+1) + 1 = x3 + 2 = (x2+1) + 2 = x2 + 3 = x1 + 4

Similary, I would like to know how to deal if there are two variable
expressions, say

x(i+1) = x(i) - (s_i) * (2^-i) * y(i)
y(i+1) = y(i) + (s_i) *(2^-i) * x(i)

for i =1, we have

x_2 = x1 - s_1 (2^-1) y_1
y_2 = y1 + s_1 (2^-1) x_1

and for i = 2 it becomes
x_3 = x1* (1 - (s_1) * (s_2) * (2^-3)) - y1* ((s_1) *  (2^-1) + (s_2)
* (2^-2))
y_3 = y1* (1 - (s_1) * (s_2) * (2^-3))  + x1* ((s_1) * (2^-1) + (s_2)
* (2^-2))

and so on .....

I have tried to use Table, Nest, and few other functional iteration
procedures. But, they seem to be giving the product of the terms
rather than substituting to give the SUM of the terms in iterative
manner.

Hope some one can help me on this.



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