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From: Ned Nedialkov
To: reliable_computing [at] interval [dot] usl.edu
Subject: bounds for a polynomial
Message-Id: <99Mar1.123935edt.45648-16386 [at] jane [dot] cs.toronto.edu>
Date: Mon, 1 Mar 1999 12:39:27 -0500
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Hi,
I am looking for a piece of software that can produce tight bounds
for the range of the polynomial
p(t) = a_0 + a_1t + ... + a_kt^k
for t \in [0, h].
That is, I need a function that has input parameters
a_0, a_1, ... a_k, and h
and returns a tight interval that contains the range of p(t) over [0,h].
Any help is greatly appreciated.
Regards,
Ned
From owner-reliable_computing [at] interval [dot] usl.edu Mon Mar 1 13:37:24 1999
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Date: Mon, 01 Mar 1999 13:38:25 -0800
To: Ned Nedialkov , reliable_computing [at] interval [dot] usl.edu
From: Nick Sahinidis
Subject: Re: bounds for a polynomial
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The BARON code provides a routine for finding the global minimum of a
univariate polynomial (no additional software is required)--switch the
coefficient signs to get the upper bound. See:
http://archimedes.scs.uiuc.edu/baron.html
At 12:39 PM 3/1/99 -0500, Ned Nedialkov wrote:
>
> Hi,
>
> I am looking for a piece of software that can produce tight bounds
>for the range of the polynomial
>
> p(t) = a_0 + a_1t + ... + a_kt^k
>
>for t \in [0, h].
>
>That is, I need a function that has input parameters
> a_0, a_1, ... a_k, and h
>and returns a tight interval that contains the range of p(t) over [0,h].
>
>Any help is greatly appreciated.
>
>Regards,
> Ned
From owner-reliable_computing [at] interval [dot] usl.edu Mon Mar 1 14:41:16 1999
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From: Kearfott Ralph B
Reply-To: Kearfott Ralph B
Subject: Re: bounds for a polynomial
To: reliable_computing [at] interval [dot] usl.edu
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And then rigorous bounds could be produced from the output of Baron
via epsilon-inflation and a verification step, provided it is certain
that Baron gives a point near the global minimum (as opposed to a
local minimizer). I'm inclined to believe it can, given that the
function is a polynomial with the coefficients known to Baron. Certainly,
for polynomials of degree 4 or less :-)
Alternately, a general interval branch and bound system, such as
GlobSol, may be used to rigorously find the minima. But that might
be more computation than you desire, if this represents a small subproblem
in a larger system.
Best regards,
Baker
> From: Nick Sahinidis
> Subject: Re: bounds for a polynomial
> Mime-Version: 1.0
>
> The BARON code provides a routine for finding the global minimum of a
> univariate polynomial (no additional software is required)--switch the
> coefficient signs to get the upper bound. See:
>
> http://archimedes.scs.uiuc.edu/baron.html
>
> At 12:39 PM 3/1/99 -0500, Ned Nedialkov wrote:
> >
> > Hi,
> >
> > I am looking for a piece of software that can produce tight bounds
> >for the range of the polynomial
> >
> > p(t) = a_0 + a_1t + ... + a_kt^k
> >
> >for t \in [0, h].
> >
> >That is, I need a function that has input parameters
> > a_0, a_1, ... a_k, and h
> >and returns a tight interval that contains the range of p(t) over [0,h].
> >
> >Any help is greatly appreciated.
> >
> >Regards,
> > Ned
R. Baker Kearfott, rbk [at] usl [dot] edu (318) 231-5346 (fax)
(318) 231-5270 (work) (318) 981-9744 (home)
From owner-reliable_computing [at] interval [dot] usl.edu Mon Mar 1 17:12:52 1999
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From: sahinidis nikolaos v
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To: Kearfott Ralph B
cc: reliable_computing [at] interval [dot] usl.edu
Subject: Re: bounds for a polynomial
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Yes, the point provided by BARON is a near-global minimum. The algorithm
used is of the branch and bound type, although all computations are done
in fixed point arithmetic and not interval arithmetic. We have used it
with polynomials up to degree 50. The BARON code for univariate
polynomials is VERY fast (even the version provided on the web is very
fast:)
Best regards, Nick
On Mon, 1 Mar 1999, Kearfott Ralph B wrote:
> And then rigorous bounds could be produced from the output of Baron
> via epsilon-inflation and a verification step, provided it is certain
> that Baron gives a point near the global minimum (as opposed to a
> local minimizer). I'm inclined to believe it can, given that the
> function is a polynomial with the coefficients known to Baron. Certainly,
> for polynomials of degree 4 or less :-)
>
> Alternately, a general interval branch and bound system, such as
> GlobSol, may be used to rigorously find the minima. But that might
> be more computation than you desire, if this represents a small subproblem
> in a larger system.
>
> Best regards,
>
> Baker
>
> > From: Nick Sahinidis
> > Subject: Re: bounds for a polynomial
> > Mime-Version: 1.0
> >
> > The BARON code provides a routine for finding the global minimum of a
> > univariate polynomial (no additional software is required)--switch the
> > coefficient signs to get the upper bound. See:
> >
> > http://archimedes.scs.uiuc.edu/baron.html
> >
> > At 12:39 PM 3/1/99 -0500, Ned Nedialkov wrote:
> > >
> > > Hi,
> > >
> > > I am looking for a piece of software that can produce tight bounds
> > >for the range of the polynomial
> > >
> > > p(t) = a_0 + a_1t + ... + a_kt^k
> > >
> > >for t \in [0, h].
> > >
> > >That is, I need a function that has input parameters
> > > a_0, a_1, ... a_k, and h
> > >and returns a tight interval that contains the range of p(t) over [0,h].
> > >
> > >Any help is greatly appreciated.
> > >
> > >Regards,
> > > Ned
>
> R. Baker Kearfott, rbk [at] usl [dot] edu (318) 231-5346 (fax)
> (318) 231-5270 (work) (318) 981-9744 (home)
>
From owner-reliable_computing [at] interval [dot] usl.edu Thu Mar 4 05:30:56 1999
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Date: Thu, 04 Mar 1999 12:16:30 +0100
To: reliable_computing [at] interval [dot] usl.edu
From: Juergen Garloff
Subject: bounds on a polynomial
Sender: owner-reliable_computing [at] interval [dot] usl.edu
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An alternative approach relies on the expansion of a polynomial into
Bernstein polynomials.
A rather complete bibliography (also on the univariate case) can be found in
R.Hungerbuehler and J.Garloff
Bounds for the range of a bivariate polynomial over a triangle
Reliable Computing 4, pp.3-13,1998.
Juergen Garloff
--------------------------------------------------------------
Prof. Dr. Juergen Garloff
Fachhochschule Konstanz/
University of Applied Sciences Konstanz
Fachbereich Informatik
Postfach 100543
D-78405 Konstanz
Germany
Tel.: +49-7531-206-597 or -627
Fax: +49-7531-206-559
email: garloff@fh-konstanz.de
URL: http://www-home.fh-konstanz.de/~garloff/
--------------------------------------------------------------
From owner-reliable_computing [at] interval [dot] usl.edu Thu Mar 4 19:46:41 1999
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From: Ned Nedialkov
To: reliable_computing [at] interval [dot] usl.edu
Subject: Summary: bounds for a polynomial
Message-Id: <99Mar4.204621edt.37913-13184 [at] qew [dot] cs.toronto.edu>
Date: Thu, 4 Mar 1999 20:46:17 -0500
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I posted the following message a few days ago:
=========================================================================
I am looking for a piece of software that can produce tight bounds
for the range of the polynomial
p(t) = a_0 + a_1t + ... + a_kt^k
for t \in [0, h].
That is, I need a function that has input parameters
a_0, a_1, ... a_k, and h
and returns a tight interval that contains the range of p(t) over [0,h].
=========================================================================
Thank you to all the people that replied.
>From the responses (so far) in this mailing list, it seems that there
is not a stand-alone function that can compute such bounds. Note that
the coefficients are not even intervals, although I have not said this
explicitly. I am not interested in downloading a package that does
other things, and somewhere it can do what I want. I need just a
function, which I can download and compile with my software. Perhaps
doing a really good job on this problem is enough for a M.Sc. project?
Regards,
Ned
From owner-reliable_computing [at] interval [dot] usl.edu Thu Mar 4 20:01:28 1999
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Date: Thu, 04 Mar 1999 17:59:42 -0800 (PST)
From: Dmitri Shiriaev
Subject: Re: Summary: bounds for a polynomial
To: reliable_computing [at] interval [dot] usl.edu
Cc: ned [at] cs [dot] toronto.edu
Reply-to: Dmitri Shiriaev
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Ned,
Unfortunately I missed this posting before.
Check out
Hammer, Hocks, Kulisch, Ratz
either
Numerical Toolbox for Verified Computing I (PASCAL-XSC version)
or
C++ Toolbox for Verified Computing (C-XSC version)
Programs in the chapter 4 do exactly what you need
The source code is freely available through
either
http://www.uni-karlsruhe.de/~iam/html/literatur/toolbox.html
or
http://www.uni-karlsruhe.de/~iam/html/literatur/c-toolbox.html
Regards
Dima
> Date: Thu, 04 Mar 1999 20:46:17 -0500
> From: Ned Nedialkov
> Subject: Summary: bounds for a polynomial
> To: reliable_computing [at] interval [dot] usl.edu
>
>
>
> I posted the following message a few days ago:
>
> =========================================================================
>
> I am looking for a piece of software that can produce tight bounds
> for the range of the polynomial
>
> p(t) = a_0 + a_1t + ... + a_kt^k
>
> for t \in [0, h].
>
> That is, I need a function that has input parameters
> a_0, a_1, ... a_k, and h
> and returns a tight interval that contains the range of p(t) over [0,h].
>
> =========================================================================
>
> Thank you to all the people that replied.
>
> From the responses (so far) in this mailing list, it seems that there
> is not a stand-alone function that can compute such bounds. Note that
> the coefficients are not even intervals, although I have not said this
> explicitly. I am not interested in downloading a package that does
> other things, and somewhere it can do what I want. I need just a
> function, which I can download and compile with my software. Perhaps
> doing a really good job on this problem is enough for a M.Sc. project?
>
> Regards,
> Ned
-- Dima --
From owner-reliable_computing [at] interval [dot] usl.edu Thu Mar 4 23:31:48 1999
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Date: Thu, 04 Mar 1999 23:27:03 -0600
To: Ned Nedialkov , reliable_computing [at] interval [dot] usl.edu
From: "R. Baker Kearfott"
Subject: Re: Summary: bounds for a polynomial
Sender: owner-reliable_computing [at] interval [dot] usl.edu
Precedence: bulk
Yes, I think it may be a good project. I did it for degree 3
as a direct method (considering various cases), when I was thinking of
providing support for splines in GlobSol. For very high degree, it
can be somewhat interesting just to find the zeros of a polynomial
with a branch and bound method. Although I completed it some time
ago, it took me a while to discover techniques that would give 20
tight verified solutions to the Wilkinson polynomial, within the
context that is now GlobSol.
Best regards,
Baker
At 08:46 PM 3/4/99 -0500, Ned Nedialkov wrote:
>
>
>I posted the following message a few days ago:
>
>=========================================================================
>
> I am looking for a piece of software that can produce tight bounds
>for the range of the polynomial
>
> p(t) = a_0 + a_1t + ... + a_kt^k
>
>for t \in [0, h].
>
>That is, I need a function that has input parameters
> a_0, a_1, ... a_k, and h
>and returns a tight interval that contains the range of p(t) over [0,h].
>
>=========================================================================
>
>Thank you to all the people that replied.
>
>>From the responses (so far) in this mailing list, it seems that there
>is not a stand-alone function that can compute such bounds. Note that
>the coefficients are not even intervals, although I have not said this
>explicitly. I am not interested in downloading a package that does
>other things, and somewhere it can do what I want. I need just a
>function, which I can download and compile with my software. Perhaps
>doing a really good job on this problem is enough for a M.Sc. project?
>
>Regards,
> Ned
>
>
---------------------------------------------------------------
R. Baker Kearfott, rbk [at] usl [dot] edu (318) 482-5346 (fax)
(318) 482-5270 (work) (318) 981-9744 (home)
URL: http://interval.usl.edu/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
USL Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------
From owner-reliable_computing [at] interval [dot] usl.edu Thu Mar 4 23:31:50 1999
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Date: Thu, 04 Mar 1999 23:27:07 -0600
To: Dmitri Shiriaev ,
reliable_computing [at] interval [dot] usl.edu
From: "R. Baker Kearfott"
Subject: Re: Summary: bounds for a polynomial
Cc: ned [at] cs [dot] toronto.edu
Sender: owner-reliable_computing [at] interval [dot] usl.edu
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Ah, yes, thanks, Dima. I'd forgot about that when I posted
my previous message. (Blush, blush)
Best regards,
Baker
At 05:59 PM 3/4/99 -0800, Dmitri Shiriaev wrote:
>Ned,
>
>Check out
>
>Hammer, Hocks, Kulisch, Ratz
>either
>Numerical Toolbox for Verified Computing I (PASCAL-XSC version)
>or
>C++ Toolbox for Verified Computing (C-XSC version)
>
>Programs in the chapter 4 do exactly what you need
>
>The source code is freely available through
>either
>http://www.uni-karlsruhe.de/~iam/html/literatur/toolbox.html
>or
>http://www.uni-karlsruhe.de/~iam/html/literatur/c-toolbox.html
>
>Regards
>Dima
>
>> Date: Thu, 04 Mar 1999 20:46:17 -0500
>> From: Ned Nedialkov
>> Subject: Summary: bounds for a polynomial
>> To: reliable_computing [at] interval [dot] usl.edu
>>
>>
>>
>> I posted the following message a few days ago:
>>
>> =========================================================================
>>
>> I am looking for a piece of software that can produce tight bounds
>> for the range of the polynomial
>>
>> p(t) = a_0 + a_1t + ... + a_kt^k
>>
>> for t \in [0, h].
>>
>> That is, I need a function that has input parameters
>> a_0, a_1, ... a_k, and h
>> and returns a tight interval that contains the range of p(t) over [0,h].
>>
>> =========================================================================
>-- Dima --
>
>
---------------------------------------------------------------
R. Baker Kearfott, rbk [at] usl [dot] edu (318) 482-5346 (fax)
(318) 482-5270 (work) (318) 981-9744 (home)
URL: http://interval.usl.edu/kearfott.html
Department of Mathematics, University of Southwestern Louisiana
USL Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------
From owner-reliable_computing [at] interval [dot] usl.edu Fri Mar 5 09:37:30 1999
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From: "Chenyi Hu"
Message-Id: <9903050935.ZM13720 [at] happy [dot] dt.uh.edu>
Date: Fri, 5 Mar 1999 09:35:21 -0800
In-Reply-To: "Angel L. Pereira"
"Javascript codes" (Feb 27, 12:17am)
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To: "Angel L. Pereira" ,
reliable_computing [at] interval [dot] usl.edu,
Angel Pereira
Subject: Re: Javascript codes
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On Feb 27, 12:17am, Angel L. Pereira wrote:
>
> I'm trying to create a javascript interval calculator abd I'm having
> problem comming with a Sin,Tan,Cos code that works with an input form.
> Can any body help me find or give me any ideas of how I can create or
> find a good code for this purpose. The main problem is that it won't let
> me use the functions more than once at the same time. Thank you.
>
Yes, we have developed an online interval calculator with Java 1.1.
Please see the websites:
http://www.mscs.mu.edu/~globsol/JavaIntervalCalc/I_C.html
or
http://gauss.dt.uh.edu/IntervalCalc/I_C.html
Chenyi Hu
--
Ph.D., Associate Professor, Computer and Mathematical Sciences
Center for Computational Science and Advanced Distributed Simulation
University of Houston-Downtown Phone: 713 221-8414
One Main Street Fax: 713 221-8086
Houston, Texas 77002 E-mail: CHu [at] uh [dot] edu
http://happy.dt.uh.edu/~hu/Hu.html