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Forum index » Science and Technology » Math » num-analysis
Newton-Kantorovich theorem proof needed
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lucas
science forum beginner


Joined: 03 Feb 2005
Posts: 7

PostPosted: Mon Jun 26, 2006 1:10 pm    Post subject: Newton-Kantorovich theorem proof needed Reply with quote
Hi to all,

i need the proof of the Newton-Kantorovich theorem, the one
that demonstrate the local convergences to a unique zero of a non
linear function of the newton method.

Here is the only page on the web that i've found that speaks about it

http://www.math.utk.edu/~ohannes/572/NK.html

I would like to know if there is some other stuff on the web about this

theorem.

Thank you!
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Peter Spellucci
science forum Guru


Joined: 29 Apr 2005
Posts: 702

PostPosted: Mon Jun 26, 2006 2:06 pm    Post subject: Re: Newton-Kantorovich theorem proof needed Reply with quote
In article <1151327414.688932.254970@c74g2000cwc.googlegroups.com>,
kingpin@freemail.it writes:
Quote:
Hi to all,

i need the proof of the Newton-Kantorovich theorem, the one
that demonstrate the local convergences to a unique zero of a non
linear function of the newton method.

Here is the only page on the web that i've found that speaks about it

http://www.math.utk.edu/~ohannes/572/NK.html

I would like to know if there is some other stuff on the web about this

theorem.

Thank you!


not on the web , but here:
J.M. Ortega, W.C. Rheinboldt: Iterative solution of nonlinear equations in several
variables, Acad. Press 1970, pages 421-423
(making use of several other theorems and lemma's , a little bit tricky but ..
optimal. there is an example which shows that the result cannot be improved
without additional assumptions on the function)

hth
peter
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lucas
science forum beginner


Joined: 03 Feb 2005
Posts: 7

PostPosted: Mon Jun 26, 2006 6:06 pm    Post subject: Re: Newton-Kantorovich theorem proof needed Reply with quote
Peter Spellucci wrote:
Quote:
In article <1151327414.688932.254970@c74g2000cwc.googlegroups.com>,
kingpin@freemail.it writes:
Hi to all,

i need the proof of the Newton-Kantorovich theorem, the one
that demonstrate the local convergences to a unique zero of a non
linear function of the newton method.

Here is the only page on the web that i've found that speaks about it

http://www.math.utk.edu/~ohannes/572/NK.html

I would like to know if there is some other stuff on the web about this

theorem.

Thank you!


not on the web , but here:
J.M. Ortega, W.C. Rheinboldt: Iterative solution of nonlinear equations in several
variables, Acad. Press 1970, pages 421-423
(making use of several other theorems and lemma's , a little bit tricky but ..
optimal. there is an example which shows that the result cannot be improved
without additional assumptions on the function)

hth
peter

The book of Ortega is referenced by the one i am using (Burlisch,
Stoer), but i don't have access to it...bad luck :(

Thank you anyway
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Arnold Neumaier
science forum Guru


Joined: 24 Mar 2005
Posts: 379

PostPosted: Tue Jun 27, 2006 7:08 am    Post subject: Re: Newton-Kantorovich theorem proof needed Reply with quote
kingpin@freemail.it wrote:
Quote:
Peter Spellucci wrote:

In article <1151327414.688932.254970@c74g2000cwc.googlegroups.com>,
kingpin@freemail.it writes:
Hi to all,

i need the proof of the Newton-Kantorovich theorem, the one
that demonstrate the local convergences to a unique zero of a non
linear function of the newton method.

Here is the only page on the web that i've found that speaks about it

http://www.math.utk.edu/~ohannes/572/NK.html

I would like to know if there is some other stuff on the web about this

theorem.

Thank you!


not on the web , but here:
J.M. Ortega, W.C. Rheinboldt: Iterative solution of nonlinear equations in several
variables, Acad. Press 1970, pages 421-423
(making use of several other theorems and lemma's , a little bit tricky but ..
optimal. there is an example which shows that the result cannot be improved
without additional assumptions on the function)

hth
peter


The book of Ortega is referenced by the one i am using (Burlisch,
Stoer), but i don't have access to it...bad luck Sad

For related results, stronger than Kantorovich, see

H. Schichl and A. Neumaier,
Exclusion regions for systems of equations,
SIAM J. Numer. Anal. 42 (2004), 383-408.
http://www.mat.univie.ac.at/~neum/papers.html#excl
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Jörgen Tegnér
science forum beginner


Joined: 27 Jun 2006
Posts: 1

PostPosted: Tue Jun 27, 2006 6:26 pm    Post subject: Re: Newton-Kantorovich theorem proof needed Reply with quote
On Mon, 26 Jun 2006 11:06:58 -0700, kingpin wrote:

Quote:

Peter Spellucci wrote:
In article <1151327414.688932.254970@c74g2000cwc.googlegroups.com>,
kingpin@freemail.it writes:
Hi to all,

i need the proof of the Newton-Kantorovich theorem, the one that
demonstrate the local convergences to a unique zero of a non linear
function of the newton method.



Quote:

not on the web , but here:
J.M. Ortega, W.C. Rheinboldt: Iterative solution of nonlinear equations
in several variables, Acad. Press 1970, pages 421-423 (making use of
several other theorems and lemma's , a little bit tricky but .. optimal.
there is an example which shows that the result cannot be improved
without additional assumptions on the function)

hth
peter

The book of Ortega is referenced by the one i am using (Burlisch, Stoer),
but i don't have access to it...bad luck :(

Thank you anyway

Another book is
V. Hutson, J. S. Pym: Applications of functional analysis and operator
theory, pages 130 and 131

Jörgen
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