Newsgroup sci.math.num-analysis 28768

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> Nice analysis, but I didn't see anything that looked like
> geometry.  So if one considers the complex Newton method as the
> iteration of a function from R^2 into R^2, does a geometric
> interpretation emerge?  I'd be keenly interested in hearing
> about that.
The geometrical interpretation of Newton's method for
complex functions is analogous to that of real functions,
except you have to deal with higher dimensions.
A complex 1-d tangent line is really a real 2-d plane in
the complex 2-d plane, i.e. real 4-d space.
You intersect the tangent line with the "z" axis. which
is also the real x-y plane and get a point.
I know this sounds weird, but in 4 dimensions two planes
generically intersect at a point.  Each plane is given
by two real equations, so you get four equations and four
unknowns.  Hope this helps.  - D
-- 
Dmitry Gokhman 
http://www.math.utsa.edu/~gokhman
Brahms Gang/Mathematics/UT San Antonio

In article <56s03l$15kk@rs18.hrz.th-darmstadt.de>,
Peter Spellucci  wrote:
>this was clearly a bad advice, since you may completely loose
>precision in the small eigenvalues, which for some applications
>are the most interesting and you reallly need them to some
>relative precison. for computing
>small eigenvalues to some precision Jacobi's method is often
>better than QR (see the work by Veselic in Numerische Mathematik)
>However, in the situation given by this posting there is no help
>other than brute force in high precision computation.
Thanks for the feedback - I also saw Pete Stewart's response to my
'erroneous' advice. I agree I jumped too quickly and was not very 
precise in my response.
However,
  when solving an ill-conditioned system of equations, one loses accuracy
and one cannot change the ill-conditioning simply by adding a multiple
of the identity since the system of equations changes.
However, for finding the eigenvalues of a matrix which is 'almost'
positive definite, e.g. the eigenvalues range from
   epsilon   to   10
then one can add a multiple of the identity and still find the
eigenvalues, i.e. add 10*I and find the eigenvalues and then
subtract 10. The question indicated (to me) that the person was having
problems with eigenvalues that became negative though he knew they
should be positive. This shift seems to correct that problem at least.
What is confusing to me is that this shift does correct the condition
number, i.e. one can find the new eigenvalues with a well conditioned
problem. E.g. if epsilon was 10^-6, then the original condition number
was 10^-5 while the new condition number is 
    2   very small.
So the accuracy of the eigenvalues found can be 'good'.
Is my reasoning wrong? If it is right - I am sorry that I explained
myself so poorly on the newsgroup.
>peterIn article , hwolkowi@orion.math.uwaterloo.ca (Henry Wolkowicz) writes:
>|> In article <328706CB.48D1@physics.uwa.edu.au>,
>|> Paul Abbott   wrote:
>|> >alan koivunen wrote:
>|> >
>|> >>I'm trying to find eigenvalues and eigenvectors of some ill-conditioned
>|> >>matrices. They are real, symmetric Toeplitz matrices, an example of 
>|> >>which is coded below:
>|> >> 
>|> >>         do i=1,N
>|> >>           do j=i,N
>|> >>             A(i,j) = exp(-2.0*(j-i)*(j-i)/((N-1)*(N-1)))
>|> >>             A(j,i) = A(i,j)
>|> >>           enddo
>|> >>         enddo
>|> >> 
>|> >>With N=13, the eigenvalue magnitudes range in value from about
>|> >>10^(-16) to about 10. The eigenvalues should be real and positive,
>|> >>but using MATLAB's eig() function and IMSL's DEVCSF routine produces
>|> >>negative (small) eigenvalues - so things aren't quite right.
>|> >> 
>|> >>So, is there anyone out there who can suggest a way to get
>|> >>eigenvalues/vectors for these troublesome matrices ? 
>|> >
>|> >Any of the Computer Algebra systems should be able to do this without
>|> >any trouble.  Here is a solution using Mathematica 3.0:
>|> >
>|> >In[1]:= Toeplitz[n_]:=Table[Exp[-2(j-i)^2/(n-1)^2], {i, n}, {j, n}]
>|> >
>|> >In[2]:= Timing[Eigenvalues[N[Toeplitz[13], 35]]]
>|> >
>|> >Out[2]= {1.8 Second, 
>|> >  {9.714289658177802948116981413446968039217238874`35, 
>|> >   2.8087047226601903588888427367223952406986690664`35, 
>|> >   0.4318113387746175560652633047322733083888887423`35, 
>|> >   0.04211529596485480041989551847174304301749342335`35, 
>|> >   0.0029201614706262355299008707132439452221134816464`35, 
>|> >   0.00015247429079448480011310165012714444499654618885`35, 
>|> >   6.150970244115566358292942430866977377286994027`35*^-6, 
>|> >   1.9294232139272084071757708173097648232541969225`35*^-7, 
>|> >   4.662923268040823404382745324585306129887057093`35*^-9, 
>|> >   8.452676823084502937530316623177950895236479696`35*^-11, 
>|> >   1.0890952782993752514438522541130430812858525505`35*^-12, 
>|> >   8.941025867763620061655233278333984110022684667`35*^-15, 
>|> >   3.531596847111418268275223468242875950227707268`35*^-17}}
>|> >
>|> >Cheers,
>|> >	Paul 
>|> >_________________________________________________________________ 
>|> >Paul Abbott
>|> >Department of Physics                       Phone: +61-9-380-2734 
>|> >The University of Western Australia           Fax: +61-9-380-1014
>|> >Nedlands WA  6907                         paul@physics.uwa.edu.au 
>|> >AUSTRALIA                           http://www.pd.uwa.edu.au/Paul
>|> >
>|> >          God IS a weakly left-handed dice player
>|> >_________________________________________________________________
>|> 
>|> 
>|> Ill-conditioned matrices mean that you will have trouble solving systems
>|> of equations, but it does not mean that you have trouble finding the
>|> eigenvalues. One simple fix to avoid worrying about negative
>|> eigenvalues, is to add
>|>     20*I
>|> to all the matrices. Then you will have a range for the eigenvalues from
>|>    20 to 30
>|> 
>|> 
>|> -- 
>|> ||Henry Wolkowicz                |Fax:   (519) 725-5441
>|> ||University of Waterloo         |Tel:   (519) 888-4567, 1+ext. 5589
>|> ||Dept of Comb and Opt           |email:  henry@orion.math.uwaterloo.ca
>|> ||Waterloo, Ont. CANADA N2L 3G1  |URL: http://orion.math.uwaterloo.ca/~hwolkowi
-- 
||Henry Wolkowicz                |Fax:   (519) 725-5441
||University of Waterloo         |Tel:   (519) 888-4567, 1+ext. 5589
||Dept of Comb and Opt           |email:  henry@orion.math.uwaterloo.ca
||Waterloo, Ont. CANADA N2L 3G1  |URL: http://orion.math.uwaterloo.ca/~hwolkowi

In the MATLAB 4 version of ode45/ode23 the error in solution x is
controlled to be less than
  tol*max(norm(x,inf),1)
so the tol value is used for both relative and absolute control.
In the preliminary beta release of the new MATLAB ODE Suite available
at www.mathworks.com on the MathWorks M-files page, the new versions
of ode45/ode23 have both relative and absolute error tolerances, and
the error in the i'th component of x is controlled to be less than
  max(rtol*abs(x(i)),atol(i))
  Hope this helps.
==== Mark Reichelt ========================= mwr@mathworks.com ===
     The MathWorks, Inc.                    info@mathworks.com
     24 Prime Park Way                http://www.mathworks.com
     Natick, MA 01760-1500                   ftp.mathworks.com
==== Tel: 508-653-1415 === Fax: 508-653-2997 =====================

In article <32911CD0.46E4@whoi.edu>, W.J.Jenkins  wrote:
>My apologies if this is a FAQ, but I was wondering whether the "tol"
>parameter in the ode23/ode45 function calls in MATLAB is an absolute
>tolerance or relative to the actual value of the function being
>modeled. For example, if the function is scaled such that at t=tf
>it is equal to, say, 10^6, should one use a value of "tol" more like
>"1" than the default of 10^-6 (for ode45)?
>
>For example, the call is 
>
>[t,y]=ode45('func',0,tf,y0,tol);
It depends on the scaling of your y-values.
The error estimate should be smaller than tol*(1+|y|) so if y is
10^6 you should still use tol=1e-6
If y on the other hand is smaller than 1, i.e. 
10^(-6) you have to a lot more stringent tol to get comparable 
results (tol=1e-12?).
--
// Homepage  http://www.dna.lth.se/home/Hans_Olsson/
// Email To..Hans.Olsson@dna.lth.se [Please no junk e-mail]

Hi all,
I would like to ask.....
To solve:
\begin{equation}
 min_{\lambda}min_{q(\lambda)}min_{S(q,\lambda)} J(\lambda,q,S)
\end{equation}
where $J(\lambda,q,S)$ is the cost function of variables $\lambda$,
$q$ and $S$.
CAN I do the above minimization using the following procedure:
(1) For fixed $\lambda$ and $q$, search for an optimal $S^{*}$.
(2) For fixed $\lambda$, search for an optimal $q^{*}$.
(3) Search for an optimal $\lambda^{*}$.
Since $S$ depends on both $\lambda$ and $q$ and $q$ depends on $\lambda$,
can I find a minimum(global/local?) use the above 3 steps?
Thanks in advance!
--
+------------------------+--------------------+
| Au Yeung Man Ching     | Rm 304             |
| Electronic Engineering | Ho Sin Hang Bldg.  |
| CUHK                   | CUHK               |
+------------------------+--------------------+
| Email : mcau@ee.cuhk.edu.hk                 |
| Homepage : http://www.ee.cuhk.edu.hk/~mcau/ |
+---------------------------------------------+

This is actually more a calculator question than a math question...
but... here goes:
If anyone out there can solve my little problem in a couple EMail
exchanges with me, I'd sure appreciate it!
I'm trying to solve the following:
Suppose I had a mortgage of $75000 @ 8%, 12 equal payments per year
for 30 years and after month 12 (I understandI would have a principal
balance remaining of $74474.50, and would have just made my 12th
payment of $550.32 (that 12 th payment consisting of $496.18 of
interest and $54.15 of principal).......
Then, let's say I made a single payment of $10000 (also assuming the
loan has no pre-payment penalties)...
How would I figure out what month I've just rocketed myself ahead
to???
With a little help, I hope I'll be able to do it on my HP - Business
10B calculator (hmmmmm...?)
Anyone willing to help, please send me an EMail.
Thanks, Flash

dennisw555@aol.com wrote:
> 
> I think there is a simple difference equation you can use to generate a
> sine wave.  Since I cannot remember it just now I won't provide anything
> that might be incorrect.
> 
> Dennis
Check out
http://www.interstice.com/~sdattalo/technical/theory/sinewave.html
Especially methods 4 and 5.
Scott

My pet dog Max died recently. I took him on our last journey together
in the car to the pet crematorium. The spooky thing about it was that
when we arrived there I noticed that the odometer was reading 87777.
Yeah, I know, it was just a coincidence .......
PF

Au_Yeung_Man_Ching wrote:
> 
> Hi all,
> 
> I would like to ask.....
> To solve:
> \begin{equation}
> 
>  min_{\lambda}min_{q(\lambda)}min_{S(q,\lambda)} J(\lambda,q,S)
> 
> \end{equation}
> 
> where $J(\lambda,q,S)$ is the cost function of variables $\lambda$,
> $q$ and $S$.
> 
> CAN I do the above minimization using the following procedure:
> 
> (1) For fixed $\lambda$ and $q$, search for an optimal $S^{*}$.
> (2) For fixed $\lambda$, search for an optimal $q^{*}$.
> (3) Search for an optimal $\lambda^{*}$.
> Since $S$ depends on both $\lambda$ and $q$ and $q$ depends on $\lambda$,
> can I find a minimum(global/local?) use the above 3 steps?
> 
> Thanks in advance!
> --
> +------------------------+--------------------+
> | Au Yeung Man Ching     | Rm 304             |
> | Electronic Engineering | Ho Sin Hang Bldg.  |
> | CUHK                   | CUHK               |
> +------------------------+--------------------+
> | Email : mcau@ee.cuhk.edu.hk                 |
> | Homepage : http://www.ee.cuhk.edu.hk/~mcau/ |
> +---------------------------------------------+
Hi,
you just consider the dependence of J on lambda, however complicated
that may be. I am assuming you can express q, S through lambda in closed
form. So, just minimize J with respect to lambda which itself enters
both directly and indirectly. If the potentially needed gradient
calculations with respect to lambda seem difficult, use numerical or
symbolic differentiation. If your problem has no constraints, then, for
example, you may use DOMIN which you find at
   ftp://plato.la.asu.edu/pub/donlp2
in both f77 and C versions.
Hope that helps,
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

Richard Li wrote:
> 
> Dear Netter:
> 
>         Can anyone give me some references concerning
> fitting a set of data to a circle  by using least square ?  Do I have
> to use parametric description ?
> 
>         Any reference either book, paper or software will be
> appreciated.
> 
> Ricky Lee
Hi,
an excellent program that does this is ODRPACK. You find a link to it
and to a nice grahical user interface on
    http://plato.la.asu.edu/guide.html
At the very beginning of the User's Guide there is a description of how
to fit data to an ellipse or circle.
Hope that helps
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

In article <328899EE.7A61@math.okstate.edu>, ullrich@math.okstate.edu 
says...
>
>Octavio Hector Juarez Espinosa wrote:
>> 
>> Hi,
>> 
>> I would like to know if there are some routines in "C" or any language
>> to read a matrix from disk.
>> I am reading element by element (519 by 519) and delays 11 minutes.
>
>        Well don't read one element at a time - read a larger chunk
>of data with each disk read.
>
>> In a PC with visual basic delays 35 minutes. I would like to know if 
there
>> are ways to speed up the process?
>
>        Don't ever use VB for anything. Borland Delphi is just as 
>convenient as VB but much faster.
>
Doesn't ANYBODY teach programming efficiency anymore?
When I learned FORTRAN, I also learned that FORTRAN stores matrices
in "column-major" order, meaning that A(1,1) was physically next
to A(2,1), A(3,1), etc.  This meant that there was a huge difference
in transferring data in that order as opposed to "row-major" order
because the transfer could be implemented with more efficient techniques.
By convention, almost all other languages use column-major
order.  In C you are looking at the actual pointer arithmetic,
so it's easy to see that the most efficient (element-by-element)
algorithm is one where you just increment the pointer between
elements.
As David implies however, block transfers are much more efficient,
as you want to minimize the number of times you actually go out
to disk.  To make block transfers happen, you might want to
do things like do a binary read of 2000 elements at a time
into a buffer, then transfer element-by-element out of the buffer.
What about your storage format?  I'm willing to wager that your
numbers are in ASCII, at 10-15 bytes per number.  Is it possible
to use a raw binary format, 4 bytes per number?  The instructions
to do this exist in every language, but they aren't always obvious
you want the low-level reading and writing as a rule.
I used to think the statement "if my code runs too slowly, you need
a bigger machine" was a joke (I laughed at a software salesman who
said it).  I'm appalled to see it has become the design philosophy for
an entire industry.  Most of what's out there could be speeded up
by an order of magnitude with little effort.
----------------------------------------------------------
Randy Poe                               
Q & D Software Solutions              Johns Hopkins University
POB 10058, Silver Spring, MD 20914    Dept. of Math. Sciences
qnd@dgsys.com                         poe@jhu.edu
We sell solutions, not just advice.
------------------------------------------------------------

Hi !
       I am developing an application that deals with line extraction
from raster images and i have the following problem:
	  - for example, given the following sequence of adjacent pixels on a
XY referential:  
    ^         xxxxxx 
 Y  |        x      x
    |        x       x
    |         x x     x
    |          x xx    x
    | x x x x      x                      x -> pixel
    |  x x x x      x
    |         x      x
    |          xx   x 
    |            xx x
    |              x
    +-------------------------------->
                                    X  
        i need to get the natural cubic spline (C2) that most
approximates these pixels.
        I would appreciate very much your advice and if such an
algorithm already exits, please send me it.
	It's URGENT...
    Thank you !	
    Joao Bastos  
*********************************************************
*  INESC - CENTRO DE SISTEMAS GRAFICOS INTERACTIVOS     *
*-------------------------------------------------------*
*                                                       *
*  JOAO IGREJAS DE BASTOS                               *
*  Eng. Informatico e de Computadores                   *
*                                                       *
*  e-mail: jpb@minerva.inesc.pt                         *
*  Tel   : +351 -1- 3100 065                            *
*  Fax   : +351 -1- 3100 009                            *
*  Morada: Av. Duque D'Avila, 23, 4-Dto  *  1000 LISBOA *
*********************************************************

Peter Spellucci wrote:
> 
> In article , Moritz Harteneck  writes:
> |> Hi,
> |>
> |> I want to minimise a least squares problem which is quadratically
> |> constrained, i.e.
> |>
> |> minimise( vAv ) under (vBv=p)
> |>
> |> where v is a n-dimensional vector of the free parameters, A describes the
> |> performance criterion and B and p the quadratic constraints.
> |>
> |> Does anybody know any good pointers?
> |>
> |> Thanks
> |>
> |>      Moritz
> |>
> |> ===========================================================================
> |> Moritz Harteneck
> |> SPD / EEE                        email: moritz@spd.eee.strath.ac.uk
> |> University of Strathclyde        http://www.spd.eee.strath.ac.uk/~moritz
> |> Glasgow G1 1XW, Scotland, U.K.
> |> Tel: ++44-(0)141-552 4400 ext 2808  Fax: ++44-(0)141-552 2487
> |>
> the solution obviously is the (an) eigenvector v corresponding to the
> (a) smallest eigenvalue of the generalized eigenvalue problem
> A v =  \lambda B v,
> normalized by vBv=p. Follows from the Lagrange multiplier rule.
> ( B hopefully positive definite) .
> for solution of generalized eigenvalue problem refer to LAPACK from netlib
> hope this helps
> peter
Right, in case B is positive definite, you can call routines SSYGV/DSYGV
from LAPACK/CLAPACK. However, if that is not the case you have to use
their nonsymmetric routines or other software available at netlib. In
particular, if your problem is
rather large and there are other difficulties such as a rank deficiency
of B, then the solution becomes a little less straightforward, but there
is software in those cases also treating it as an eigenvalue problem
which may help and would not make it necessary to use LS-software.
-- 
Hans D. Mittelmann			http://plato.la.asu.edu/
Arizona State University		Phone: (602) 965-6595
Department of Mathematics		Fax:   (602) 965-0461
Tempe, AZ 85287-1804			email: mittelmann@asu.edu

Where is it?
n8tm@aol.com wrote in article <19961114070300.CAA15939@ladder01.news.aol.com>...
> I have prepared a draft (chapter for proposed book)? paper concerning
> performance issues of C vs FORTRAN, which anyone is welcome to look at and
> perhaps criticize constructively.  About 45kB text.
> Tim
> 

Does anybody know where to find an implementation of red-black trees
in FORTRAN
Thanks a lot.
Leo.
-- 
Leonid Shilkrot                                   shilkrot@engin.umich.edu
Dept. of Materials Science                        (313)213-0807(h)
University of Michigan                            (313)647-2780(w)
Ann Arbor, MI 48109-2136                          (313)763-4788(fax)

Hi,
I would like to know where I can get info about testing that results
during numerical
integration are within the tolerance set by the user.  It seems to me
that as the
integrator chops the problem into small sections, the tolerance required
for each
section must be some fraction of the desired tolerance for the whole
integral.
Channing

--
บบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบบ
 Sanjeev R. Nagarkar                   211 Lakeside Drive, Apt.#103  
			               Greenbelt, MD 20770
       				       W:(301) 405  
 http://www.wam.umd.edu/~sanjeevn      H:(301) 474 7605
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Hi, would someone please help? I am looking for some input/help on this question:
Say, I have a conditional density f(a|b) which satisfies log-supermodularity.
(supermodularity iff always positive cross partials, and log-supermodular iff
log of the function is supermodular)
I then have another conditional density g(a|x(b)) which i know to
be log-supermodular. x is monotone increasing in b.
can I use the two conditional density and the monotonicity of x in b 
to get something about the conditional density h(b|x(b))?
Results that I am trying to manipulate in doing this are:
1. products of log-supermodular functions are always log-supermodular
2. integrals of log-supermodualr functions are log-supermodular
Any leads/help will be appreciated
Thanks
Mitali Das
mitali@mit.edu
Keywords: 

Hi, would someone please help? We are looking for some input/help on this question:
Say, we have a conditional density f(a|b) which satisfies log-supermodularity.
(supermodularity iff always positive cross partials, and log-supermodular iff
log of the function is supermodular)
I then have another conditional density g(a|x(b)) which i know to
be log-supermodular. x is monotone increasing in b.
can I use the two conditional density and the monotonicity of x in b 
to get something about the conditional density h(b|x(b))?
Results that I am trying to manipulate in doing this are:
1. products of log-supermodular functions are always log-supermodular
2. integrals of log-supermodualr functions are log-supermodular
Any leads/help will be appreciated
Thanks
Mitali Das and Andrea Repetto

I am a Mechanical Engineering student with an interest in Math.  I am 
currently trying to compile a list of as many simple expressions, numbers, 
or equations that are equal to one.  I have just started, but here's what I 
have:
(sin n)^2 + (cos n)^2  where n is an angle
i^2
-i^4
Normal Distribution
Student's T Distribution
0.99...  (9's repeating ad infinitum)
Derivative of X where X is any independent variable
If you know of any, please e-mail me.  Thanks in advance.
Whitney Roberts

In article  aroberts@usq.edu.au (Tony Roberts) writes:
>In article <3287C6B6.224@sumppu.fmi.fi>, Olaf Amm  wrote:
>
>> Hi,
>> 
>> I am looking for an algorithm that is able to estimate the curl and
>> divergence of a vector field from measurements of that field, given on
>> irregularly spaced points.
>> It would be best if that algorithm could do it without gridding the data
>
>Could do a radial basis function fit of each component, then differentiate
>the fits.  
>
>For scalar data u_i at n points x_i (in m-dimensions) fit
>u(x)=\sum_{j=1}^n a_jf(|x-x_j|)  +b.x +c
>where f(r)=r^2\log r or f(r)=r^3.
>
>There are n+m+1 unknowns: a_j, vector b, c:
>n equations come from u(x_i)=u_i
>m equations from \sum_{j=1}^na_jx_j=0
>and 1 from   \sum_{j=1}^n a_j=0
>This is a symmetric system of equations.  For economy chose about a dozen
>data points in the neighbourhood of the place you want to estimate the
>derivatives.
If you want to go this way, may I suggest that you look at splines
that may "adapt" to the amount of div and curl (or the variations in these)
in your data. A starting point in the Div-Curl splines of Amodei and Benbourhim
(J Approx Theory 1991). The get yourself a spline solving package
like Chong Gu's rkpk. I'm not necessarily suggesting this will always
be the best way - it's something I've played with from time to time.
regards
D. Suter
David Suter - Dept. of Electrical and
Computer Systems Engineering, Monash University,
Clayton, Vic. 3168, Australia
ph 9905 5682 Fax 9905 3454
( ISD prefix 61 3 )
http://www.batman.eng.monash.edu.au
-- 
David Suter - Dept. of Electrical and
Computer Systems Engineering, Monash University,
Clayton, Vic. 3168, Australia
ph 9905 5682 Fax 9905 3454

Austin Lee wrote:
> I need a f77 or c source code to
> compute double precision complex Gamma function.
See http://www.pd.uwa.edu.au/Keith/specfunc.m4
Keith
-- 
Keith Briggs, Department of Physics, University of Western Australia,
Nedlands, Australia 6907.  Phone (+09) 380 2728.  Fax (+09) 380 1014.

In article <56lu27$7r2@mcmail.CIS.McMaster.CA>,
Zdislav V. Kovarik  wrote:
>In article <56l5f5$noa@newstand.syr.edu>, Tom Scavo  wrote:
>:
>:So if one considers the complex Newton method as the
>:iteration of a function from R^2 into R^2, does a geometric
>:interpretation emerge?
>
> The desired extension to complex Newton's method takes place in a 
>4-dimensional space...
> If you have four-dimensional imagination (which I don't), everything will
>be immediately clear. And before you explode with anger over such a
>disappointing answer...
Yes, the answer is disappointing, but not so much so that
I should "explode with anger". :-)  I'll just keep searching
until I find a geometric interpretation of the complex Newton
method in less than four dimensions.  (Such an interpretation is
evidently not well-known.)
Thanks,
-- 
Tom Scavo
trscavo@syr.edu
http://web.syr.edu/~trscavo/