Namir, Byte and REXX
09-10-2018, 04:00 PM
Post: #10
 Thomas Klemm Senior Member Posts: 1,551 Joined: Dec 2013
RE: Namir, Byte and REXX
We can use the Complex-Step Derivative Approximation mentioned in Derivatives on HP 42S to calculate with a single subroutine call both $$f(x)$$ and $$f'(x)$$ in Newton's method:

$$x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}$$

Code:
00 { 34-Byte Prgm } 01▸LBL "NEWTON" 02 STO "x" 03 RCL "h" 04 COMPLEX 05 XEQ "FF" 06 COMPLEX 07 RCL÷ "h" 08 ÷ 09 STO- "x" 10 RCL "x" 11 END

For the equation $$2x^2+3x-12=0$$ of the given example this program can be used:
Code:
00 { 19-Byte Prgm } 01▸LBL "FF" 02 2 03 RCL× ST Y 04 3 05 + 06 × 07 12 08 – 09 END

Initialisation

1E-8
STO "h"

Iteration

5
XEQ "NEWTON"

y: 2.30434782609
x: 2.69565217391

R/S
y: 0.77053902071
x: 1.92511315320

R/S
y: 1.10972947392E-1
x: 1.81414020581

R/S
y: 2.40138878229E-3
x: 1.81173881703

R/S
y: 1.12553786619E-6
x: 1.81173769149

R/S
y: 2.47260969077E-13
x: 1.81173769149

Cheers
Thomas
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 Messages In This Thread Namir, Byte and REXX - Massimo Gnerucci - 09-07-2018, 11:32 AM RE: Namir, Byte and REXX - Zaphod - 09-08-2018, 06:34 PM RE: Namir, Byte and REXX - Geoff - 09-10-2018, 03:07 PM RE: Namir, Byte and REXX - Duane Hess - 09-09-2018, 05:36 AM RE: Namir, Byte and REXX - Massimo Gnerucci - 09-09-2018, 10:34 AM RE: Namir, Byte and REXX - toml_12953 - 09-10-2018, 12:11 PM RE: Namir, Byte and REXX - toml_12953 - 09-10-2018, 12:14 PM RE: Namir, Byte and REXX - Massimo Gnerucci - 09-10-2018, 01:26 PM RE: Namir, Byte and REXX - Thomas Klemm - 09-10-2018, 12:52 PM RE: Namir, Byte and REXX - toml_12953 - 09-11-2018, 12:35 PM RE: Namir, Byte and REXX - Thomas Klemm - 09-10-2018 04:00 PM