Difference between power method and normalised power method
i've been trying to learn about power method. I don't understand why some people normalise the eigenvector and why some people just use a form of scaling. For example:
$bf{q^{(k)}} = frac{Abf{q^{(k-1)}}}{|Abf{q^{(k-1)}}|_2}$ being the normalised version.
$bf{q^{(k)}} = {Abf{q^{(k-1)}}}$ which is then scaled down by dividing by an element of $q$.
What effect will this have on finding the dominating eigenvalue? For example can you use the Rayleigh Quotient on either of the two eigenvectors? Many thanks.
linear-algebra eigenvalues-eigenvectors
asked Nov 29 at 0:29
kp1897
11
add a comment |
i've been trying to learn about power method. I don't understand why some people normalise the eigenvector and why some people just use a form of scaling. For example:
$bf{q^{(k)}} = frac{Abf{q^{(k-1)}}}{|Abf{q^{(k-1)}}|_2}$ being the normalised version.
$bf{q^{(k)}} = {Abf{q^{(k-1)}}}$ which is then scaled down by dividing by an element of $q$.
What effect will this have on finding the dominating eigenvalue? For example can you use the Rayleigh Quotient on either of the two eigenvectors? Many thanks.
linear-algebra eigenvalues-eigenvectors
asked Nov 29 at 0:29
kp1897
11
add a comment |
i've been trying to learn about power method. I don't understand why some people normalise the eigenvector and why some people just use a form of scaling. For example:
$bf{q^{(k)}} = frac{Abf{q^{(k-1)}}}{|Abf{q^{(k-1)}}|_2}$ being the normalised version.
$bf{q^{(k)}} = {Abf{q^{(k-1)}}}$ which is then scaled down by dividing by an element of $q$.
What effect will this have on finding the dominating eigenvalue? For example can you use the Rayleigh Quotient on either of the two eigenvectors? Many thanks.
linear-algebra eigenvalues-eigenvectors
asked Nov 29 at 0:29
kp1897
11
i've been trying to learn about power method. I don't understand why some people normalise the eigenvector and why some people just use a form of scaling. For example:
$bf{q^{(k)}} = frac{Abf{q^{(k-1)}}}{|Abf{q^{(k-1)}}|_2}$ being the normalised version.
$bf{q^{(k)}} = {Abf{q^{(k-1)}}}$ which is then scaled down by dividing by an element of $q$.
What effect will this have on finding the dominating eigenvalue? For example can you use the Rayleigh Quotient on either of the two eigenvectors? Many thanks.
linear-algebra eigenvalues-eigenvectors
linear-algebra eigenvalues-eigenvectors
asked Nov 29 at 0:29
kp1897
11
asked Nov 29 at 0:29
kp1897
11
asked Nov 29 at 0:29
kp1897
11
asked Nov 29 at 0:29
kp1897
11
asked Nov 29 at 0:29
kp1897
11
11
add a comment |
add a comment |
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%2f3017984%2fdifference-between-power-method-and-normalised-power-method%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3017984%2fdifference-between-power-method-and-normalised-power-method%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
