Hello Hauke -
That sounds very interesting -- I too would be
glad to receive a copy (if it's not asking too
much - you could use PM in that case);
btw, I'm a fellow citizen (former Math teacher,
long retired = a.D., besides other occupations)
losely following forum discussions (not much of a
contributor lately due to personal reasons).
-M
At 2020-10-15 14:20, you wrote:
Hello Stefan, I guess by your name and email
adress that youâre from austria so you could
read and understand German. I took lecture notes
last year in a Numerics course here at the
university of Jena and implemented nearly all of
the algorithms using J, with coloured J lines
interspersed with the notes. (typeset with LaTeX
and the minted package) I used explicit code in
some places but most of it is tacit and thus
without for. style loops. But of course there
need to be ^: style loops in many places. EDIT:
I just did a /for\. search and it turned out I
didnât use it at all For example, the
line for the newton representation of the
lagrange polynomial reads Newton =: 1 : â[: +/
(nbase pmul u divdiff)\â NB. pmul aus Beispiel
1.40 where 1.40 is a clickable back-reference.
All the other names have been defined in the
current section. Up to that point there are no
explicit definitions at all. If youâre
interested, Iâll ask if I may send you the pdf
file (I guess it will be okay) in case youâre
interested. cheers, Hauke Am 15.10.20 um 15:50
schrieb Stefan Baumann: > Dear all. > Recently I
stumbled upon the Newton polynomial and took it
as a practice to > implement it without using
loops, but failed. I first didn't get a grab
on > how to create the matrix used in >
https://en.wikipedia.org/wiki/Newton_polynomial#Main_idea,
and eventually > came up with code following >
https://en.wikipedia.org/wiki/Newton_polynomial#Application:
> > NB. Newton polynomial > > np=: 4 : 0 > >
a=. {. y > > for_i. }.>:i.#x do. > > y=. (2
(-~)/\ y) % i ({:-{.)\ x NB. Divided
differences > > a=. a, {. y NB. Coefficients are
the topmost entries > > end. > > NB. Convert the
summands aáµ¢(x-xâ)
(x-xáµ¢ââ) of the
polynomial > > NNB. from multiplier-and-roots to
coefficients form and add them up > > +/@,:/
p."1 (;/a) ,. (<''), }:<\ x > > ) > > x=: _3r2
_3r4 0 3r4 3r2 > > y=: 3&o. x > > load'plot' > >
load'stats' > > plot (];(x np y)&p.) steps _1.5
1.5 30 > > I also tried replacing the loop with
fold F:. but again was not able to do > so.
Anyone out there who can enlighten me? > > Many
thanks. Stefan. >
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