10 REM RADICE DI COS(X)-X CON NEWTON PROTETTO DA BISEZIONE - FULL
20 REM DATA: ESTREMO A, ESTREMO B, TOLLERANZA
30 DATA 0,1,0.000000001
40 LET LOW=0:LET HIGH=0:LET TOL=0
50 READ LOW,HIGH,TOL
60 IF LOW>=HIGH OR TOL<=0 THEN GOTO 400
70 IF TOL<0.000000000001 THEN GOTO 400
80 LET XVAL=LOW:LET FX=0:LET DERIV=0
90 LET FLEFT=0:LET FRIGHT=0:LET PROPOSE=0:LET RESID=0
100 LET ITER=0:LET NEWTON=0:LET BISECT=0:LET CONVERGE=0
110 LET SCALED=0
120 GOSUB 370:FLEFT=FX
130 XVAL=HIGH:GOSUB 370:FRIGHT=FX
140 IF FLEFT*FRIGHT>0 THEN GOTO 400
150 XVAL=(LOW+HIGH)/2
160 WHILE CONVERGE=0
170 GOSUB 370:ITER=ITER+1:RESID=ABS(FX)
180 PRINT "ITER;",ITER,";",XVAL,";",FX,";",HIGH-LOW,CRLF
190 IF RESID<=TOL THEN GOTO 310
200 IF ITER>=100 THEN GOTO 410
210 IF FLEFT*FX<=0 THEN GOTO 230
220 LOW=XVAL:FLEFT=FX:GOTO 240
230 HIGH=XVAL:FRIGHT=FX
240 IF ABS(DERIV)<0.000000000001 THEN GOTO 280
250 PROPOSE=XVAL-FX/DERIV
260 IF PROPOSE<=LOW OR PROPOSE>=HIGH THEN GOTO 280
270 NEWTON=NEWTON+1:GOTO 290
280 PROPOSE=(LOW+HIGH)/2:BISECT=BISECT+1
290 XVAL=PROPOSE
300 WEND
310 SCALED=INT(XVAL*1000000000+0.5)
320 PRINT "ROOT;",XVAL,";",SCALED,";",RESID,CRLF
330 PRINT "STEPS;",ITER,";",NEWTON,";",BISECT,CRLF
340 IF XVAL<LOW OR XVAL>HIGH OR RESID>TOL THEN GOTO 410
350 PRINT "NEWTON TEST OK",CRLF
360 END
370 FX=COS(XVAL)-XVAL
380 DERIV=-SIN(XVAL)-1
390 RETURN
400 PRINT "ERRORE PARAMETRI O INTERVALLO NEWTON",CRLF:END
410 PRINT "ERRORE CONVERGENZA NEWTON",CRLF:END