Information about Newton's method at a certain stepNewton's Method for Roots of PolynomialsProve or disprove - Newton's method convergence in higher dimensionsHow to solve for the interval of convergence in Newton's Method?In practice, what does it mean for the Newton's method to converge quadratically (when it converges)?Newton's method for nth roots of complex numbersUsing of Newton's method to find a complex root of a polynomialUse Newton's method on a constant?Convergence of a variant of Newton's MethodConditions for Newton's method to converge.Global convergence with Newton method for nonlinear systems
Does the reader need to like the PoV character?
A Trivial Diagnosis
How can I write humor as character trait?
Were Persian-Median kings illiterate?
How to get directions in deep space?
How does electrical safety system work on ISS?
Does "he squandered his car on drink" sound natural?
What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?
How many arrows is an archer expected to fire by the end of the Tyranny of Dragons pair of adventures?
How can ping know if my host is down
What (the heck) is a Super Worm Equinox Moon?
Review your own paper in Mathematics
How would you translate "more" for use as an interface button?
Mimic lecturing on blackboard, facing audience
How do you make your own symbol when Detexify fails?
How do I tell my boss that I'm quitting soon, especially given that a colleague just left this week
Are Captain Marvel's powers affected by Thanos breaking the Tesseract and claiming the stone?
Do we have to expect a queue for the shuttle from Watford Junction to Harry Potter Studio?
Biological Blimps: Propulsion
What is the difference between lands and mana?
Non-trope happy ending?
Has the laser at Magurele, Romania reached a tenth of the Sun's power?
"It doesn't matter" or "it won't matter"?
15% tax on $7.5k earnings. Is that right?
Information about Newton's method at a certain step
Newton's Method for Roots of PolynomialsProve or disprove - Newton's method convergence in higher dimensionsHow to solve for the interval of convergence in Newton's Method?In practice, what does it mean for the Newton's method to converge quadratically (when it converges)?Newton's method for nth roots of complex numbersUsing of Newton's method to find a complex root of a polynomialUse Newton's method on a constant?Convergence of a variant of Newton's MethodConditions for Newton's method to converge.Global convergence with Newton method for nonlinear systems
$begingroup$
We are preforming Newton's method with step $F'(x_n)Delta x=-F(x_n)$, $x_n+1=Delta x +x_n$, where $F:mathbbR^n rightarrow mathbbR^n$. We can assume that it will converge. At a give time we know the values of $x_0$ up to $x_k$.
Can we use $||F'(x_0)-F'(x_k)||$ to say anything about the convergence?
newton-raphson
asked Mar 14 at 16:49
MathiasMathias
64
$endgroup$
add a comment |
$begingroup$
We are preforming Newton's method with step $F'(x_n)Delta x=-F(x_n)$, $x_n+1=Delta x +x_n$, where $F:mathbbR^n rightarrow mathbbR^n$. We can assume that it will converge. At a give time we know the values of $x_0$ up to $x_k$.
Can we use $||F'(x_0)-F'(x_k)||$ to say anything about the convergence?
newton-raphson
asked Mar 14 at 16:49
MathiasMathias
64
$endgroup$
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57
add a comment |
$begingroup$
We are preforming Newton's method with step $F'(x_n)Delta x=-F(x_n)$, $x_n+1=Delta x +x_n$, where $F:mathbbR^n rightarrow mathbbR^n$. We can assume that it will converge. At a give time we know the values of $x_0$ up to $x_k$.
Can we use $||F'(x_0)-F'(x_k)||$ to say anything about the convergence?
newton-raphson
asked Mar 14 at 16:49
MathiasMathias
64
$endgroup$
We are preforming Newton's method with step $F'(x_n)Delta x=-F(x_n)$, $x_n+1=Delta x +x_n$, where $F:mathbbR^n rightarrow mathbbR^n$. We can assume that it will converge. At a give time we know the values of $x_0$ up to $x_k$.
Can we use $||F'(x_0)-F'(x_k)||$ to say anything about the convergence?
newton-raphson
newton-raphson
asked Mar 14 at 16:49
MathiasMathias
64
asked Mar 14 at 16:49
MathiasMathias
64
asked Mar 14 at 16:49
MathiasMathias
64
asked Mar 14 at 16:49
MathiasMathias
64
asked Mar 14 at 16:49
MathiasMathias
64
64
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57
add a comment |
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148238%2finformation-about-newtons-method-at-a-certain-step%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148238%2finformation-about-newtons-method-at-a-certain-step%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
I think one can construct a parameterised example where the norm of the difference is arbitrary and the sequence of iterates is the same, so no. The reason is that the norm is too 'coarse'. In practice, it gives an estimate of how 'linear' the problem is.
$endgroup$
– copper.hat
Mar 14 at 16:57