'===========================================================================
' Subject: NEWTON'S ITERATIVE METHOD         Date: 11-12-99 (20:11)       
' Author:  The ABC Programmer                Code: QB, QBasic, PDS        
' Origin:  voxel@edmc.net                  Packet: ALGOR.ABC
'===========================================================================
' Newton's iterative method for solving square roots of numbers
' by William Yu (11-12-99)  e-mail: voxel@edmc.net

DEFDBL A-Z

CLS
NUM = 2348734     '' Find square root of this number

DEF FNF (X)
  FNF = X ^ 2 - NUM
END DEF

DEF FNDF (X)
  FNDF = 2 * X
END DEF

DEF FNNEWTON (X)
  FNNEWTON = X - FNF(X) / FNDF(X)
END DEF

X = 1              '' Initial guess

DO
  Y = FNNEWTON(X)
  IF X = Y THEN EXIT DO
  X = Y
LOOP

PRINT "The square root of"; NUM; "is"; X
PRINT "Real value is: "; SQR(NUM)