(HP41) Iterated function with convergence to square root (Heron method)
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04-25-2023, 03:21 PM
(This post was last modified: 04-27-2023 05:09 PM by floppy.)
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(HP41) Iterated function with convergence to square root (Heron method)
Since RPN and FOCAL with it stack is efficient for iterated functions, here a posting of the iterated function of aN=(an + b/an) / 2 which result will be SQRT(b).
Other way to represent this is f(x,y)=(x+y/x,y). Then f(f(f(..(a0,b))))=(sqrt(b),b). The start value a0 can be anything (result will have the negativ sign if the start value a0<0). Nothing really new: - no register used in comparison to the programm available in page 11 in https://literature.hpcalc.org/community/...ram-de.pdf ) - start value can be defined (will be defined as b if a0=0) - no calculation done if b=0 Code: ; SQRT as iterated function, "möbius transform like" = only + * or / HP71B 4TH/ASM/Multimod, HP41CV/X/Y & Nov64d, PILBOX, HP-IL 821.62A & 64A & 66A, Deb11 64b-PC & PI2 3 4 w/ ILPER, VIDEO80, V41 & EMU71, DM41X |
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Messages In This Thread |
(HP41) Iterated function with convergence to square root (Heron method) - floppy - 04-25-2023 03:21 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - C.Ret - 04-25-2023, 05:51 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - Thomas Klemm - 04-25-2023, 06:29 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - floppy - 04-25-2023, 06:34 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - floppy - 04-25-2023, 06:30 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - Thomas Klemm - 04-25-2023, 06:56 PM
RE: (HP41) Iterated function with convergence to square root (Heron method) - Thomas Klemm - 04-25-2023, 07:20 PM
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