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.