1  REM  ****  HP BASIC PROGRAM LIBRARY  *******************************
2  REM
3  REM        ROOTNL:   FINDS THE ROOTS OR FIXED POINTS OF A 
4  REM                  NON-LINEAR FUNCTION
5  REM        36697 REV  A   10/73
6  REM
7  REM  ****  CONTRIBUTED PROGRAM  ************************************
9000  REM  ROOTNL--LOCATES THE ROOTS OF A NON-LINEAR FUNCTION
9002  PRINT 
9004  PRINT "SUPPLY STARTING VALUE."
9006  INPUT X
9008  IF X=999999. THEN 9999
9010  PRINT 
9012  PRINT " X","F(X)"
9014  PRINT 
9016  GOSUB 9050
9018  LET X1=X
9020  LET X=Y
9022  FOR I=1 TO 10
9024  LET X2=X1
9026  LET X1=X
9028  LET Y1=Y
9030  GOSUB 9050
9032  PRINT X,Y
9034  IF Y=Y1 THEN 9054
9036  LET X=(X2*Y-X*Y1)/(Y-Y1)
9038  NEXT I
9040  PRINT "SUPPLY 0 FOR 10 MORE ITERATIONS, 1 TO RESTART."
9042  INPUT W
9044  IF W=0 THEN 9022
9046  IF W=1 THEN 9002
9048  STOP 
9050  LET Y=SIN(X)-COS(X)
9052  RETURN 
9054  PRINT 
9056  PRINT "DIVISION BY 0."
9058  PRINT "SUPPLY A NEW STARTING VALUE OR TYPE 999999 TO STOP."
9060  GOTO 9006
9999  END 
