Thanks Hauke, would be very interested in the pdf file. Actually I'm a German living in Austria (Vienna). Ciao. Stefan.
On Thu, Oct 15, 2020 at 4:21 PM Hauke Rehr <[email protected]> wrote: > Hello Stefan, > > I guess by your name and email adress that you’re 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 didn’t > use it at all > For example, the line for the newton representation of the > lagrange polynomial reads > Newton =: 1 : ’[: +/ (nbase pmul u divdiff)\’ 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 you’re interested, I’ll ask if I may send you the pdf file > (I guess it will be okay) in case you’re 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 aᵢ(x-x₀)…(x-xᵢ₋₁) of the polynomial > > > > NB. 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. > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > ---------------------- > mail written using NEO > neo-layout.org > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
