create table temp_res (a integer, res number);
insert into temp_res values(1, 1);
insert into temp_res values(2, 1.41421288939285);
insert into temp_res values(3, 1.73205078513617);
insert into temp_res values(4, 1.99999999999617);
insert into temp_res values(5, 2.23606797658102);
insert into temp_res values(6, 2.4494897130809);
insert into temp_res values(7, 2.64575095945042);
insert into temp_res values(8, 2.82842712474403);

SQL> with data as (select rownum val from dual connect by level<=8)
  2  select val,sqrt(val) from data
  3  /

       VAL  SQRT(VAL)
---------- ----------
         1          1
         2 1.41421356
         3 1.73205081
         4          2
         5 2.23606798
         6 2.44948974
         7 2.64575131
         8 2.82842712

8 rows selected.

SELECT 'Stop bei i=' ||i||' a=' ||a|| ' Delta=' || d ||' f(x)=' ||f erg FROM dual
MODEL 
  DIMENSION BY (1 as na)
  MEASURES (0 as d, 1 as f, 0 as i, 8 as a)
  RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1]) - d[1]) <1E-100
( 
 i[1] = ITERATION_NUMBER+1,
 --newton-raphson method: x(n+1)=x(n)-(1-a/x**2)/(2a/x**3)
 d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
 f[1] = f[1]-d[1]
 );

ERG                                                                             
--------------------------------------------------------------------------------
Stop bei i=11 a=8 Delta=0 f(x)=2,82842712474619009760337744841939615714         

SELECT 'Stop bei x=' ||x||' i=' ||i||' a=' ||a|| ' Delta=' || d ||' f(x)=' ||f erg FROM dual
MODEL 
  DIMENSION BY (1 as na)
  MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
  RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1]) - d[1]) <1E-100
( 
 i[1] = ITERATION_NUMBER+1,
 d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
 f[1] = f[1]-d[1],
 x[1] = for z in 2..9 loop
           x[1]=f[i]+z
	end loop
 )

 x[1] = for z in 2..9 loop
           x[1]= f[1]+z
	end loop

 x[1] = sum[ for z between 2..9, x[1]=f[1]+z ]

SELECT 'SQRT at inc='||inc||' x=' ||x||' ' erg FROM dual
MODEL 
  DIMENSION BY (1 as inc)
  MEASURES (8 as x)
  RULES 
( 
  x[FOR inc FROM 2 TO 10 INCREMENT 1] =  1/2*(x[1]/x[cv()-1]+x[cv()-1])
 );

ERG
---------------------------------------------------------
SQRT at inc=1 x=8 
SQRT at inc=2 x=4,5 
SQRT at inc=3 x=3,13888888888888888888888888888888888889 
SQRT at inc=4 x=2,84378072763028515240904621435594886923 
SQRT at inc=5 x=2,8284685718801466821819618416725070015 
SQRT at inc=6 x=2,82842712504986412995671609183567406561 
SQRT at inc=7 x=2,82842712474619009761967942719569409644 
SQRT at inc=8 x=2,82842712474619009760337744841939615714 
SQRT at inc=9 x=2,82842712474619009760337744841939615714 
SQRT at inc=10 x=2,82842712474619009760337744841939615714 

SELECT 'Stop bei x=' ||x||' i=' ||i||' a=' ||a|| ' Delta=' || d ||' f(x)=' ||f erg FROM dual
MODEL 
  DIMENSION BY (1 as na)
  MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
  RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1]) - d[1]) <1E-100
( 
 i[1] = ITERATION_NUMBER+1,
 d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
 f[1] = f[1]-d[1],
 x[1] = for z in 2..9 loop   -|
           x[1]=f[1]+z        | how can I write this as an interation give that 
                                this is within another iteration step?
	end loop             -|
 )

x[ANY] = sum(f[na between 2 and 9])

SQL> ed
Wrote file afiedt.buf

  1  with at as (select rownum rn from dual connect by level <=10)
  2  SELECT rn,' f(x)=' ||f erg
  3  FROM at
  4  MODEL
  5    PARTITION BY (at.rn)
  6    DIMENSION BY (1 as na)
  7    MEASURES (0 as d, 1 as f, 0 as i, at.rn as a)
  8    RULES ITERATE (9)
  9  (
 10   i[1] = ITERATION_NUMBER+1,
 11   d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
 12   f[1] = f[1]-d[1]
 13   )
 14* order by 1
SQL> /

        RN ERG
---------- ----------------------------------------------
         1  f(x)=1
         2  f(x)=1.41421356237309504880168872420969807857
         3  f(x)=1.73205080756887729352744634150587236694
         4  f(x)=2
         5  f(x)=2.23606797749978969640917366873127623544
         6  f(x)=2.44948974278317809819728407470589139196
         7  f(x)=2.64575131106459059050161575363926042571
         8  f(x)=2.82842712474619009760337744841939615714
         9  f(x)=3
        10  f(x)=3.16227766016837933199889354443271853371

10 rows selected.

SQL> 

 
x[1] = for z in 2..9 loop   -|
           x[1]=f[1]+z        | how can I write this as an interation give that 
                                this is within another iteration step?
	end loop             -|

x[1] = f[1]+9

SELECT 'Stop bei x=' ||x||' i=' ||i||' a=' ||a|| ' Delta=' || d ||' f(x)=' ||f erg FROM dual
MODEL 
  DIMENSION BY (1 as na)
  MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
  RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1]) - d[1]) <1E-100
( 
 i[1] = ITERATION_NUMBER+1,
 d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
 f[1] = f[1]-d[1],
 -- x = z*x + power(2,z)   for z in 2..9  
 x[1] =  ( 2*x[1] + power(2,2) )
        +( 3*x[1] + power(2,3) )
        +( 4*x[1] + power(2,4) )
        +( 5*x[1] + power(2,5) )
        +( 6*x[1] + power(2,6) )
        +( 7*x[1] + power(2,7) )
        +( 8*x[1] + power(2,8) )
        +( 9*x[1] + power(2,9) )
)

SQL> SELECT 'Stop bei x=' ||x||' i=' ||i||' a=' ||a|| ' Delta=' || d ||' f(x)=' ||f erg FROM dual
  2  MODEL 
  3    DIMENSION BY (1 as na)
  4    MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
  5    RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1]) - d[1]) <1E-100
  6  ( 
  7   i[1] = ITERATION_NUMBER+1,
  8   d[1] = (1-a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
  9   f[1] = f[1]-d[1],
 10   -- x = z*x + power(2,z)   for z in 2..9  
 11   x[1] =  ( 2+3+4+5+6+7+8+9)*x[1] + power(2, ( 2+3+4+5+6+7+8+9))   
 12  )
 13  /

ERG
--------------------------------------------------------------------------------
Stop bei x=489588034328312985544036450304 i=11 a=8 Delta=0 f(x)=2.82842712474619
009760337744841939615714

measure_column [ { { condition
                   | expr
                   | single_column_for_loop
                   }
                     [, { condition
                        | expr
                        | single_column_for_loop
                        }
                     ]...
                 | multi_column_for_loop
                 }
               ]

Note: The outer square brackets are part of the syntax.
      In this case, they do not indicate optionality.

 x[1] =  ( 2*x[1] + power(2,2) )
        +( 3*x[1] + power(2,3) )
        +( 4*x[1] + power(2,4) )
        +( 5*x[1] + power(2,5) )
        +( 6*x[1] + power(2,6) )
        +( 7*x[1] + power(2,7) )
        +( 8*x[1] + power(2,8) )
        +( 9*x[1] + power(2,9) )

measure_column [ { { condition
                   | expr
                   | single_column_for_loop
                   }
                     [, { condition
                        | expr
                        | single_column_for_loop
                        }
                     ]...
                 | multi_column_for_loop
                 }
               ]

Note: The outer square brackets are part of the syntax.
      In this case, they do not indicate optionality.