Question

someone good at numerical analysis..........i need help urgently

Answer 1

if p and q are the roots of x^2+ax+b=0,then show that the iteration \[x _{n+1}=-(b/(x _{n}+a))\]
will converge near x=p if p<q

Answer 2

what does x_n mean ?

Answer 3

the approximated value of root at nth iteration

Answer 4

i am assuming this corresponds to newton's method of finding roots// please verify,,

Answer 5

if thats the case, we know

x_n+1 = x_n -[ f(x_n)/(f'(x_n) ]
= x_n - [( x_n^2 + ax_n +b) / ( 2x_n +a)]
= (x_n ^2 -b)/(2x_n +a)
according to what we are given
we see
-b/(x_n +a) = (x_n ^2 -b)/(2x_n +a)

-2bx_n -ab = x_n ^3 -bx_n +ax_n ^2 -ab
-2bx_n = x_n ^3 - bx_n - ax_n ^2

since x_n is not equal to 0,

-2b = x_n^2 -b - ax_n
x_n^2 - ax_n + b =0

o.O

lol !!
sorry,,maybe i did something wrong,,gotta go,,will get back to this asap..