'*****************************************************
'* Program to demonstrate Newton's method subroutine *
'* ------------------------------------------------- *
'* Reference: BASIC Scientific Subroutines, Vol. II  *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1]. *
'* ------------------------------------------------- *
'* SAMPLE RUN:                                       *
'*                                                   *
'* (Example: find a real root of (x+1)^5)            *
'*                                                   *
'* Input the initial guess:                          *
'*                                                   *
'*    X0 = 0                                         *
'*                                                   *
'* Convergence factor: 1e-6                          *
'*                                                   *
'* Maximum number of iterations: 30                  *
'*                                                   *
'*                                                   *
'* The calculated zero is X = -.9984525574007144     *
'*                                                   *
'* The associated Y value is Y = 8.872622688643E-015 *
'*                                                   *
'* The number of steps was: 30                       *
'*****************************************************
defint i-n
defdbl a-h,o-z
cls
print
print " Input the initial guess:"
print
input "    X0 = ",x0
print
input " Convergence factor : ",e
print
input " Maximum number of iterations: ",m

gosub 2000  'Call Newton routine

print
print " The calculated zero is X = "; x
print
print " The associated Y value is Y = "; y
print
print " The number of steps was: "; n
print
end
'*************************************
1000 ' Function subroutine
  y = 1+5*x+10*x*x+10*x^3+5*x^4+x^5
  'derivative
  y1 = 5+20*x+30*x*x+20*x^3+5*x^4
  return
'*************************************

'***********************************************
'*         Newton's method subroutine          *
'* ------------------------------------------- *
'* This routine calculates the zeros of a      *
'* function Y(x) by Newton's method.           *
'* The routine requires an initial guess, x0,  *
'* and a convergence factor, e. Also required  *
'* is alimit on the number of iterations, m.   *
'***********************************************
2000 n=0
  'Get y and y1
2100 x=x0 : gosub 1000
  'Update estimate
  x0=x0-y/y1
  n=n+1
  if n>=m then return
  if ABS(y/y1)>e then goto 2100
  x=x0
return

'End of file Newton1.bas