Subject: fitting vertices on a surface to a biparametric spline
From: rms@nih.gov (Ron Summers)
Date: Fri, 06 Dec 1996 22:46:24 GMT
I am seeking software to fit vertices on a surface to a biparametric
spline. The vertices are of the form (x,y,z) and are scattered about
the surface (i.e., are not along contour lines or along
cross-sections). I would like to fit them to a biparametric spline
(i.e., a function of (u,v)). Can anyone point me to relevant software
or texts?
Ron Summers
rms@nih.gov
Subject: Re: Greatest Common Denominator
From: hbaker@netcom.com (Henry Baker)
Date: Sat, 7 Dec 1996 17:59:59 GMT
In article <584nqd$h7@news01.btx.dtag.de>, Winnie_Heitele@t-online.de
(Winnie Heitele) wrote:
> Dear net users,
> I'm looking for an algorithm to extract the "Greatest Common
> Denominator" out of a sequence of numberic values. Thus I
> would be glad if someone knows this kind of algorithms or
> can give me an idea of a good booklet.
> Thanks in advance.
> --
>
> Best Regards
> Winnie
ans: Euclid's algorithm.
For non-negative rational integers a,b,c:
gcd(a,b,c) = gcd(a,gcd(b,c))
gcd(a,b) = gcd(b,a)
gcd(a,0) = a
gcd(a,b) = gcd(mod(a,b),b)
I.e.,
(a>=0, b>=0)
gcd(a,b) = if b=0 then a else gcd(b,mod(a,b))
mod(a,b) = a - floor(a/b)*b
floor(q) = greatest integer <= q.
See Knuth, "Fundamental Algorithms, Vol. I".
Subject: Re: Available Partial SVD code?
From: "John C. Nash"
Date: Sat, 7 Dec 1996 17:30:19 -0500
On 2 Dec 1996, Norm Lehtomaki wrote:
> In article <32a345f8.0@newshost.atk.com>,
> norm@atk.com (Norm Lehtomaki) writes:
> > What is the state of the art in computing only the left or right singular
> > vectors of the k largest singular values of a nxm complex matrix where
> > n > m > k. Is there efficient code for this available? I am aware of
> > the psvd.f in netlib. It uses the smallest singular values and has
> > k = m. I'm looking for k < m.
>
>
> Actually, I'm in error here. psvd.f does use k < m but I'm still interested
> in getting a selectable subspace associated with the largest singular
> values and not the smallest.
>
Seymour Shlien & I published a short paper in the Computer Journal in
1987 with two compact algorithms. One of these was put in the 1990
(and 1996 Japanese) editions of my Compact Numerical Methods for
Computers.
I don't have the exact ref. of Nash & Shlien to hand. Sorry.
JN
John C. Nash, Professor of Management, Faculty of Administration,
University of Ottawa, 136 Jean-Jacques Lussier Private,
P.O. Box 450, Stn A, Ottawa, Ontario, K1N 6N5 Canada
email: jcnash@uottawa.ca, voice mail: 613 562 5800 X 4796
fax 613 562 5164, Web URL = http://macnash.admin.uottawa.ca
Subject: Re: pointers on numerical analysis history?
From: jdebord@MicroNet.fr (Jean Debord)
Date: Sat, 07 Dec 1996 16:32:25 GMT
kamthan@cs.concordia.ca (KAMTHAN pankaj) wrote:
>Could anybody suggest any pointers to articles on the historical
>evolution of any of the various aspects of numerical analysis:
>LU decompostion, Newton's method, Simpson's rule, etc.?
Here is the reference of an excellent book (in French) :
Jean-Luc Chabert et al (1994)
Histoires d'Algorithmes
Editions Belin, 8 Rue Ferou, 75006 Paris
ISBN 2-7011-1346-6
I don't know if there is an English edition of this book, however.
Sincerely
Jean Debord
Faculte de Medecine
Limoges, France
Subject: Asymptotic expansion and norms
From: Rene Aid
Date: Sun, 08 Dec 1996 16:53:02 +0100
Does anyone know where I can find theorem on the composition
of asymptotic expansion of vector valued functions and norms
of these fonctions ?
Typically, I want to know wether this proposition holds :
if f(e,x) = f_0(x) + f_1(x) e + ... + O(e^p)
then || f(e,x) || = || f_0(x) || + G_1(x) e + ... + O(e^p),
for any good norm.
Thanks,
Rene Aid
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