Numerical analysis help plz!!!! (who can prove this?)

[secured]

hi every1... I am started taking now Numerical Anaylsis course... and till now am very confused... very...

does any1 know how to solve this problem please??

Let g(x) = -0.0001 x2 + x and p0 = 1, and consider fixed-point iteration

(a) show that p0 > p1 > … > pn > pn+1 > …
(b) show that pn > 0 for all n.
(c) Since the sequence {pn} is decreasing and bounded below, it has a limit. What is the limit?


10x for ur help...

1 more thing... does any1 hav the solutions manual of
"Numerical Methods using matlab" 3rd or 4th edition?
by: John H. Mathews And Kurtis D. Fink
Prentice Hall


plz answer asap...
peace

 

[elnenez]

I think the problem is not well stated.
How \[p_i\] is defined?
Is there any relation between \[g(x)\] and \[p_0\]?

 

[mmatica]

g(x) = -a x^2 + x, 0 < a < 1.

(a) p_n - p_(n+1) = a (p_n)^2 > 0

(b) Using induction, 0< p_n <= 1

(c) Denoting p = lim p_n
one obtains using the continuity of g in

p_(n+1) = g(p_n)

that p=g(p) ==> p=0.