Other iterative inethods

vVhen providing current nrnnipulations with

2 2

1 - p2 + a 2 = 1 - p2 + x ( 1 - po )

o o 1 _ x2

1 - PZ

1-x^2

a2

x2 ,

we find that

a2(x+po)

CY=----

x (1 - p~)

1 + XPo

l+CY=---1-x (^2) '
1

B=--

l +CY

x(x +Po)

1 - x^2

and, consequently, the expression for the function

1 1 p^2 +cy-a~ 'I

f(B)= l+CYPo+ l+CY JCY2+a2= o.

( 1 + CY) Po

Taking into account that

2? 2 2 a^2

p 0 +CY - Ci~ = ( 1 +CY) - ( l - p 0 +a ) = l +CY - 2

x

it is plain to show that

II

x+ Po

Sii:::; --

1 + XPo

1 - PZ Po+ X

1 - x2 = Po 1 - x2 ,

1-x^2

for T = T 0 ---

1 + XPo

739

The meaning of this is that a solution of problem (30) satisfies the
estin1ate

with

(39)
x+Po
p=
1 + x Po '

11 Yn - 1l 11 < P^71 11 Yo - U 11

T 0 ( 1 - x")

x = ----;====;;o /3 T=T=----

J11 12 + ,; '