A somewhat different Newton solver (HP35s)

[Ángel Martin]

Nicely done, it piqued my curiosity so I went ahead and jotted down the following 41Z version of the same concept.- About 30 steps in this proof of concept; which expects the function name in ALPHA, h in Y and the xo guess (a real value) in X.

Code:

01  LBL "ZNWT"   
02  ASTO 00    ; F.Name
03  X<>Y       
04  STO 01     ; h
05  CLX        ; ensure Im(z)=0
06  X<>Y   
07  LBL 00     ; loop
08  FS? 10     ; show value?
09  ZAVIEW     ; yes
10  ZSTO 01    ; save Zo = xo + 0i
11  XEQ IND 00 ; calculate f(Zo)
12  ZSTO 02    ; save f(Zo)
13  ZRCL 01    ; Zo
14  RCL 01     ; h
15  X<>Y    
16  XEQ IND 00 ; calculate f(Zo+i.h)
17  X<>Y       ; Im[f(Zo+i.h)]
18  RCL 01     ; h
19  /          ; f'(xo)
20  ST/ 04     ; divides Re[f(Zo)] by it
21  ST/ 05     ; divides Im[f(Zo)] (which should be zero anyway)
22  ZRCL 01    ; Zo
23  ZENTER^   
24  ZRCL 02    ; f(xo)/f'(xo)
25  Z-         ; x1
26  Z#W?       ; converged?
27  GTO 00     ; no, next iteration
28  CLA        ; yes, reset ALPHA
29  ARCL 00
30  END        ; done

The execution shows the successive values of the root if user flag 10 is set (a la PPC-ROM).
Convergence criteria always uses 9 decimal places - irrespective of the display FIX settings.

The function is to be programmed using 41Z functions (definitely a super-set of those in the 35S), as a complex equation.

To use Dieter's same example:

Code:

01  LBL "Z1"
02  Z^3
03  LASTZ
04  Z^2
05  LASTZ
06  Z+
07  Z-
08  ,5
09  +
10  END

Results:

ALPHA, "Z1", ALPHA
0.1, ENTER^, 2, XEQ "ZNWT" -> 1.451605963
0.1, ENTER^, 0, XEQ "ZNWT" -> 0.403031717
0.1, ENTER^, -2, XEQ "ZNWT"-> -0.854637680

Supposedly more accurate results would be obtained with smaller values of h...

Cheers,
ÁM