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convergence of QR-algorithm
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Jason Wells
science forum beginner


Joined: 24 Mar 2005
Posts: 1

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: New Proof Of The Fundamental Theorem Of Calculus Reply with quote
John,
If indeed your Average Tangent Theorem is true, then it would be a
far more efficient way of proving both the Mean Value Theorem as well
as the FTOC (fundamental theorem of calculus). And yes it wouold
provide a direct link between the derivative and integral.

I can't see any flaws with it but some of your opponents, eg. Graeme
McRae and others don't seem to think so. Perhaps your most vehement
arguments were those on Cut-the-knot wher you refuted the
mathematician Vladimir. You have a very abrupt style of responding to
objections - if I may, you may try posing your responses as questions
rather than 'attacks' as has been interpreted by most.
I think McRae is not necessarily an opponent either because he plainly
admits he cannot understand your theorem.

I think you are on to something big here - at least as far as
understanding is concerned. Personally I have failed to see the direct
link even though I've always known there is one. An Archimedes may
have indeed known of differentiation should your theorem be proved.

Jason Wells.

On 21 Nov 03 06:09:04 -0500 (EST), John Gabriel wrote:
Quote:
Your web page is interesting but I think there is a far easier way to
prove not only the FTOC but every important calculus theorem - my
average tangent theorem not only defines and proves the mean value
theorem for the first time since Isaac Newton, but it proves both
parts of the Ftoc in such simple mathematics so that even a high
school student can understand it. It also proves finite differences,
Taylor's Theorem, Quadrature/Cubature, Arc Lengths, Newton's
Approximation Formula and much more. I invite you to check out:

a
href="http://www.geocities.com/john_gabriel">http://www.geocities.com/john_gabriel</a

John Gabriel
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Anon
science forum Guru Wannabe


Joined: 03 Jun 2005
Posts: 184

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: help for differential trigonometrical equation Reply with quote
On Thu, 10 Feb 2005 17:13:05 +0000 (UTC), thataung@yahoo.com (hlamoe)
wrote:

Quote:
sinwt+coswt=?

Perhaps you want: sin(wt) + cos(wt) = sqrt(2) sin( wt + Pi/4 )
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hlamoe
science forum beginner


Joined: 24 Mar 2005
Posts: 1

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: help for differential trigonometrical equation Reply with quote
sinwt+coswt=?
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Herman Rubin
science forum Guru


Joined: 25 Mar 2005
Posts: 730

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Is there any: Simulation based parameter estimation method? Reply with quote
In article <42338265.C2CB5631@Xsdynamix.com>, bv <bvoh@Xsdynamix.com> wrote:
Quote:
Neon wrote:

How do you develop parameter estimation for complex system with some
output observations, wich can only be simulated other than modeled with
close form formula?

It's done routinely since few, if any, real world problems come with a
close form solution, except, homework problems stupefied for Matlab type
sw usage. It's a subject of active research, and is also (hopefully) at
the very core of modern cae/cad toolsets. Search for "inverse problems"
to learn more.

There are many statistical procedures of this type as well.
Most Bayesian type problems need this, and it can be used
for classical procedures as well. There is a large
statistical literature here.


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
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Jeremy Watts
science forum Guru Wannabe


Joined: 24 Mar 2005
Posts: 239

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Is this M=U^T D U factorization also called Crout factorization? Reply with quote
<hzmonte@hotmail.com> wrote in message
news:1107306054.765186.161800@l41g2000cwc.googlegroups.com...
Quote:
In the 1987 edition of Thomas Hughes's "The Finite Element Method:
Linear Static And Dynamic Finite Element Analysis" (Chapter 11), he
describes a procedure that he called Crout Elimination and Crout
factorization. It factorizes a symmetric and positive definite matrix
into a nonsingular upper triangular matrix U, with unit diagonal
entries, and a diagonal matrix D. The algorithm does not look like the
Crout algorithm people usually refer to in performing a LU
factorization of a general matrix. And the resulting U and D certainly
are not the L and U that we get when we do a LU factorization. Do some
people also use "Crout" to refer to this M = U^T D U factorization?

there is an alternative to the LU decomposition, whereby a third matrix is
generated that only has non-zero elements along its diagonal. Its quite
easy to take an upper triangular matrix, and decompose that into a
'diagonal' matrix, and another upper triangular matrix which has 1's along
its diagonal.

This is someties used as a test for positive definiteness because if the
elements of the diagonal matrix are positive then indeed the matrix
decomposed is itself positive definite.

Anyway basically for a matrix A, then A = LU = LDU'

where D is a diagonal matrix, and U' another upper triangular matrix which
has 1's along its diagonal

If the matrix is symmetric or hermittian, then this LDU' decomposition
becomes LDL^T , which looks like what you have there.

>
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Gert Van den Eynde
science forum beginner


Joined: 18 May 2005
Posts: 15

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Cubic Splines Versus B-Splines Reply with quote
beliavsky@aol.com wrote:

Quote:
Michael Hill wrote:
Hi, folks.

I am looking for clarification on the differences between Cubic
Splines and b-splines. What are the differences and strengths between
the two? When would I use one method over the other?

At this point, based on my own reading, it seems that the Cubic
Spline
method is better for producing a "smoother-looking" curve (although
the algorithm is said to be bigger than for a b-spline). So then why
would anybody EVER use a b-spline?
Assuming that Cubic Splines are better, somebody please direct me to
good-quality source code for a Cubic Spline algorithm.

Carl de Boor "wrote the book" on splines, and his Fortran 77 codes for
b-splines and cubic splines are at http://www.cs.wisc.edu/~deboor/pgs/
. There are also spline codes in Fortran 90, C++, and Matlab at
http://www.csit.fsu.edu/~burkardt/ .

Also check out http://netlib.org/dierckx and the book


Curve and Surface Fitting with Splines
P. Dierckx
Oxford University Press 1995
ISBN 019853440X

bye,
gert
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Peter Spellucci
science forum Guru


Joined: 29 Apr 2005
Posts: 702

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Solubility of a mathematical function... Reply with quote
In article <6efac814.0502011311.48fc7f13@posting.google.com>,
orthopaedic.md@gmail.com (Jwang) writes:
Quote:
Hello...I'm a high school student interested to know if there is a
general method to test the ability for a particular function to be
solved. For example, it is apparent 2^x=x has no real solutions as can
be demonstrated graphically. However, I'm just curious if there is a
general method for determining whether or not a function can be
solved...

Thanks...

unfortunately, the answer is "no", even for functions of one variable.
there are sufficient criteria of different flavor and power, but nothing
truly general.
for example: f continous and there are a,b such that f(a)*f(b)<0.
f continuously differentiable and 0<c<|f'(x)| for all x and some fixed c
f a polynomial of odd degree
etc
hth
peter
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Victor Eijkhout
science forum addict


Joined: 12 May 2005
Posts: 78

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Cubic Splines Versus B-Splines Reply with quote
<beliavsky@aol.com> wrote:

Quote:
Carl de Boor "wrote the book" on splines,

Let me quote from page 314, the section "PostScript on things not
covered":

The book covers only univariate spline approximations [...] This is to
me the most painful omission since multivariate approximation is, at
present, an exiting area of research, and practical results,
particularly from the finite element method and from Computer Aided
Design, are already available.

In other words: his book, while mathematically fantastic, does not cover
the kind of splines you use in graphics.

V.
--
email: lastname at cs utk edu
homepage: www cs utk edu tilde lastname
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Roy W. Wright
science forum beginner


Joined: 24 Mar 2005
Posts: 2

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Math won't survive the next 10 years Reply with quote
I'd better stock up on these:
http://www.cafepress.com/math_shirts/250903


Quote:
I am a time traveller from the future and I must tell you that math won't
survive the year 2015. All current knowledge will proven false, outlawed,
and banned worldwide and members of the underground who secretly study
math and get caught will be arrested and shot.
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James Van Buskirk
science forum beginner


Joined: 14 Jun 2005
Posts: 17

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: (Epsilon OT) Weird Intel FP performance variation Reply with quote
"Phil Hobbs" <pcdh@SpamMeSenseless.us.ibm.com> wrote in message
news:1107r5rbdhvb61d@corp.supernews.com...

Quote:
Any ideas about what's going on?

PIIIs sure are slow for denormals, aren't they?

--
write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, &
6.0134700243160014d-154/),(/'x'/)); end
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Madhusudan Singh
science forum beginner


Joined: 14 May 2005
Posts: 28

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Integrable singularity Reply with quote
beliavsky@aol.com wrote:

Quote:
Madhusudan Singh wrote:
beliavsky@aol.com wrote:

Madhusudan Singh wrote:
I wish to numerically integrate a real function with an
integrable
singularity.

What are the recommended methods for accomplishing the above ?

Numerical Recipes in Fortran 77, section 4.4 has a discussion and
code
for this. You can download the pdf file from
http://www.library.cornell.edu/nr/ . One can use an "open"
quadrature
formula, which does not evaluate the function at the endpoints of
the
integration region. Alternatively, a variable transformation can
often
remove the singularity.

Thanks for the info.

The function I need to work on needs to be integrated in [0,\infty)
and has
a singularity at a finite x0 \in [0,\infty).

Assuming x0 is known, one can separately compute the integrals on
(0,x0) and (x0,+inf). The "classic" Fortran (77) quadrature library is
quadpack at http://www.netlib.org/quadpack/ , and I think that library
has codes to handle integrals with endpoint singularities and with
semi-infinite domains.
Some quadpack codes have been translated to F90-style codes by Alan
Miller -- search "integration" at http://users.bigpond.net.au/amiller/
.

Many Fortran codes for numerical quadrature by Alan Genz, a researcher
in the subject, are at
http://www.math.wsu.edu/faculty/genz/software/software.html . John
Burkhardt has some quadrature codes at
http://www.csit.fsu.edu/~burkardt/f_src/f_src.html .

Thanks for the links Smile
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Guest
PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Graham's Scan Time Complexity Reply with quote
For the vertices that we pop off, comparison can be charged to the pop
operation.
For every vertex, we then are left with one extra orientation test,
which in total causes
only O(n) instructions.

It's just whom you charge the operation, that gets you O(n) Smile
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a. volgenat
science forum beginner


Joined: 24 Mar 2005
Posts: 1

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Volgenant Jonker TSP algorithm Reply with quote
On Fri, 05 Apr 2002 04:22:23 GMT, Condoor wrote:
Quote:

Almost every article on the Traveling Salesman Problem has the
following
reference in the bibliography.

[ Volgenant T., Jonker R. (1982). "A Branch and Bound Algorithm for
the
Symmetric Traveling Salesman Problem based on the 1-Tree
Relaxation.",
European Journal of Operations Research. ]

It must have been quite an article! Can anybody tell me where an
english
copy of this famous article might be obtained?

I've also heard that there used to be a Pascal version of the
algorithm
available on the web. Does anyone know where a download of that could
be
found?

Thanks



have you received any answer on this message.
If not, let me know and I can inform you further.
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N.Gangadhar
science forum beginner


Joined: 24 Mar 2005
Posts: 1

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: Bandwidth reduction of a non-symmetric matrix Reply with quote
On 18 Nov 2004 06:35:26 -0800, Peter Verveer wrote:
Quote:
I would like to reduce a sparse non-symmetric (but square) matrix by
reordering the columns and rows, to a band diagonal form. I know that
there is algorithms available to do this for a symmetric matrix (i.e.
toms 582 from netlib), but I have not found anything for
non-symmetric
matrices.

Cheers, Peter

--
Dr Peter J Verveer
European Molecular Biology Laboratory
Meyerhofstrasse 1
D-69117 Heidelberg
Germany
Tel. +49 6221 387 8245
Fax. +49 6221 397 8306

respected sir,
i'm from india.. i'm a post graduate
student,doing master of technology...sir now i'm doing my project...In
my project i have to reduce nonsymmetric matrix to symmetric
matrix...i've been searched somany site to get algorithms regarding
this,but i couldn't find...can i get any algorithms from u sir?...can
i get any other sources?...i should be thankfull to u sir if i get
repply from u?
Thanking u sir,
ur's faithfully,
N.Gangadhar.
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Raj Kumar
science forum beginner


Joined: 24 Mar 2005
Posts: 1

PostPosted: Thu Mar 24, 2005 7:28 pm    Post subject: Re: inversion of pd-matrix ? Reply with quote
sir /mam
i am an student of master of personnel management and industrial
relations at Banaras Hindu University Varanasi India. i want to get
informatin about what in pd matrix, why is it their in industries, how
is is done.
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Google
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