Linda, here's a pretty good Newton's method adverb:
newt =: 1 : 0
t =. y
h =. 1 % 512
whilst. t ~: s do.
s =. t
t =. s - +: h * (u s) % (u s + h) - u s - h
h =. h % 2
end.
t
)
(2 - *:) newt 1 NB. function on left, first root guess on right
1.414213562
--Kip
Sent from my iPad
> On Feb 25, 2014, at 12:44 AM, "Linda Alvord" <[email protected]> wrote:
>
> I've been trying to remember Newton's Method and I came upon this:
>
> f=: 13 :'(A=:1 + ] - *:)N^:y]1'
> f
> 3 : '(A=:1 + ] - *:)N^:y]1'
>
> f 4
> 1597r987
> A 4
> _11
>
> _11 N^:4]1
> |nonce error: N
> | -u% u d.1
>
> It has been such a long time since I have seen a nonce error that I thought
> it was worth sharing!
>
> Linda
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Nimp O
> Sent: Monday, February 24, 2014 8:08 AM
> To: [email protected]
> Subject: Re: [Jprogramming] A Tale Without End
>
> Another nice way to get a lot of digits from the golden ratio is using
> Newton's Method.
>
> In : http://www.jsoftware.com/jwiki/Essays/Newton%27s%20Method
> N=: 1 : '- u % u d. 1'
>
> correct50 =: '1.61803398874989484820458683436563811772030917980576'
> 0j50 ": (1 + ] - *:) N^:7 ] 1
> 1.61803398874989484820458683436563811772030917980576
> correct50 -: 0j50 ": (1 + ] - *:) N^:7 ] 1
> 1
>
>
> # correct1000 =:
> '1.6180339887498948482045868343656381177203091798057628621354486227...'
> 1002
>
> correct1000 -: 0j1000 ": (1 + ] - *:) N^:12 ] 1
> 1
> You can get 50 correct digits in 7 iterations and 1000 digits in 12!
>
>
>
>
>
>> Here are the first 100 digits using this J function:
>>
>> 0j101 ":B
> 1.61803398874989484820458683436563811772030917980576286213544862270526046281
>> 890244970720720418939113748
>>
>> Linda
>
>
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