'*****************************************************
'*  Program to demonstrate Secant 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 f(x)=(x+1)^5 )     *
'*                                                   *
'* Input the initial guesses:                        *
'*                                                   *
'*    X0 = -2                                        *
'*    X1 = 0                                         *
'*                                                   *
'* Convergence factor: 1e-6                          *
'* Maximum number of iterations: 50                  *
'*                                                   *
'*                                                   *
'* The calculated zero is X = -1                     *
'*                                                   *
'* The associated Y value is Y = 0                   *
'*                                                   *
'* The number of steps was: 3                        *
'*                                                   *
'*****************************************************
defint i-n
defdbl a-h,o-z
cls
print
print " Input the initial guesses:"
print
input "    X0 = ",x0
input "    X1 = ",x1
print
input " Convergence factor : ",e
input " Maximum number of iterations: ",m

gosub 2000  'Call secant routine

print
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
  return
'*************************************

'***********************************************
'*          Secant method subroutine           *
'* ------------------------------------------- *
'* This subroutine calculates the zeroes of a  *
'* function Y(x) using the secant method.      *
'* Two initial guess are required, x0 and x1,  *
'* and a convergence criterion, e. Also requi- *
'* red is the maximum number of iterations, m. *
'* The root is returned in x, the number of    *
'* iterations performed in n.                  *
'***********************************************
2000 n=0
  'Start iteration
2100 x=x0 : gosub 1000
  y0=y : x=x1
  'Get next point
  gosub 1000
  y1=y
  'Calculate new estimate
  'Guard against y1-y0 too small
  if ABS(y1-y0)<0.001 then y1=y1+0.001
  x=(x0*y1-x1*y0)/(y1-y0)
  n=n+1
  'Test for convergence
  if n>=m then return
  if ABS(x1-x0)<e then return
  'Update positions
  x0=x1 : x1=x
  goto 2100
return

'End of file secant.bas