Convergence of the Newton-Raphson method applied to a nonlinear system
I'm working on a nonlinear system of 2 equations and try to solve it with the Newton-Raphson method.
I have a function $f(x,y)$. In order to use the method, I have to find a starting vector $(x,y)$. But the method will only converge for specific starting vectors.
Is there a formula that gives the convergence of the Newton-Raphson method on a system of equations ?
Thank you all.
convergence nonlinear-system newton-raphson
asked Dec 5 '18 at 16:28
LucLuc
1
add a comment |
I'm working on a nonlinear system of 2 equations and try to solve it with the Newton-Raphson method.
I have a function $f(x,y)$. In order to use the method, I have to find a starting vector $(x,y)$. But the method will only converge for specific starting vectors.
Is there a formula that gives the convergence of the Newton-Raphson method on a system of equations ?
Thank you all.
convergence nonlinear-system newton-raphson
asked Dec 5 '18 at 16:28
LucLuc
1
add a comment |
I'm working on a nonlinear system of 2 equations and try to solve it with the Newton-Raphson method.
I have a function $f(x,y)$. In order to use the method, I have to find a starting vector $(x,y)$. But the method will only converge for specific starting vectors.
Is there a formula that gives the convergence of the Newton-Raphson method on a system of equations ?
Thank you all.
convergence nonlinear-system newton-raphson
asked Dec 5 '18 at 16:28
LucLuc
1
I'm working on a nonlinear system of 2 equations and try to solve it with the Newton-Raphson method.
I have a function $f(x,y)$. In order to use the method, I have to find a starting vector $(x,y)$. But the method will only converge for specific starting vectors.
Is there a formula that gives the convergence of the Newton-Raphson method on a system of equations ?
Thank you all.
convergence nonlinear-system newton-raphson
convergence nonlinear-system newton-raphson
asked Dec 5 '18 at 16:28
LucLuc
1
asked Dec 5 '18 at 16:28
LucLuc
1
asked Dec 5 '18 at 16:28
LucLuc
1
asked Dec 5 '18 at 16:28
LucLuc
1
asked Dec 5 '18 at 16:28
LucLuc
1
1
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
As long as you pick even a somewhat reasonable guess, the method should find the closest root. If the equations were linear, and you never encounter a situation where you divide by zero, you won't even have to use a reasonable guess.
$$
{displaystyle x_{n+1}=x_{n}-m{frac {f(x_{n})}{f'(x_{n})}}.}
$$
answered Dec 5 '18 at 16:36
nessness
375
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
add a comment |
No, in general there is no easy way to determine whether or not Newton-Raphson will converge for a given starting value, other than to try it. The region of convergence can be very complicated, and may have a fractal boundary.
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
add a comment |
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%2f3027294%2fconvergence-of-the-newton-raphson-method-applied-to-a-nonlinear-system%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
As long as you pick even a somewhat reasonable guess, the method should find the closest root. If the equations were linear, and you never encounter a situation where you divide by zero, you won't even have to use a reasonable guess.
$$
{displaystyle x_{n+1}=x_{n}-m{frac {f(x_{n})}{f'(x_{n})}}.}
$$
answered Dec 5 '18 at 16:36
nessness
375
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
add a comment |
As long as you pick even a somewhat reasonable guess, the method should find the closest root. If the equations were linear, and you never encounter a situation where you divide by zero, you won't even have to use a reasonable guess.
$$
{displaystyle x_{n+1}=x_{n}-m{frac {f(x_{n})}{f'(x_{n})}}.}
$$
answered Dec 5 '18 at 16:36
nessness
375
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
add a comment |
As long as you pick even a somewhat reasonable guess, the method should find the closest root. If the equations were linear, and you never encounter a situation where you divide by zero, you won't even have to use a reasonable guess.
$$
{displaystyle x_{n+1}=x_{n}-m{frac {f(x_{n})}{f'(x_{n})}}.}
$$
answered Dec 5 '18 at 16:36
nessness
375
As long as you pick even a somewhat reasonable guess, the method should find the closest root. If the equations were linear, and you never encounter a situation where you divide by zero, you won't even have to use a reasonable guess.
$$
{displaystyle x_{n+1}=x_{n}-m{frac {f(x_{n})}{f'(x_{n})}}.}
$$
answered Dec 5 '18 at 16:36
nessness
375
answered Dec 5 '18 at 16:36
nessness
375
answered Dec 5 '18 at 16:36
nessness
375
answered Dec 5 '18 at 16:36
nessness
375
375
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
add a comment |
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
The problem is that I use the N-R method in a program and I don't know some parameters of my function $f(x,y)$. That means I cannot make a "reasonable guess". What I do know is that $f(x,y)$ is nonlinear. I would need a formula that determines wether the method converges in terms of the function $f(x,y)$.
– Luc
Dec 5 '18 at 16:51
add a comment |
No, in general there is no easy way to determine whether or not Newton-Raphson will converge for a given starting value, other than to try it. The region of convergence can be very complicated, and may have a fractal boundary.
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
add a comment |
No, in general there is no easy way to determine whether or not Newton-Raphson will converge for a given starting value, other than to try it. The region of convergence can be very complicated, and may have a fractal boundary.
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
add a comment |
No, in general there is no easy way to determine whether or not Newton-Raphson will converge for a given starting value, other than to try it. The region of convergence can be very complicated, and may have a fractal boundary.
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
No, in general there is no easy way to determine whether or not Newton-Raphson will converge for a given starting value, other than to try it. The region of convergence can be very complicated, and may have a fractal boundary.
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
answered Dec 5 '18 at 16:59
Robert IsraelRobert Israel
319k23208458
319k23208458
add a comment |
add a comment |
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%2f3027294%2fconvergence-of-the-newton-raphson-method-applied-to-a-nonlinear-system%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
