Reduced complexity of matrix inversion of sum of rank 1 matrices: $M^{-1} = left( I + sum limits_{i=1}^{K}...
$begingroup$
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learninglearning
346
$endgroup$
add a comment |
$begingroup$
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learninglearning
346
$endgroup$
add a comment |
$begingroup$
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learninglearning
346
$endgroup$
How to reduce the complexity of matrix inversion of sum of rank 1 matrices, not only arithmetic but also run time?
$M^{-1} = left( I + sum limits_{i=1}^{K} alpha_i A_i right)^{-1} $
where $A_i in mathbb{C}^{N times N}$, ${rm rank}left(A_i right) = 1$, and $alpha_i in mathbb{R}$.
For instance, the suggestion here is apprently reducing the arithmetic complexity but not the run time (I mean it will take $N$ iterations to find the matrix inverse)? What other alternatives do we have?
linear-algebra computational-complexity numerical-linear-algebra
linear-algebra computational-complexity numerical-linear-algebra
asked Nov 28 '18 at 12:00
learninglearning
346
asked Nov 28 '18 at 12:00
learninglearning
346
asked Nov 28 '18 at 12:00
learninglearning
346
asked Nov 28 '18 at 12:00
learninglearning
346
asked Nov 28 '18 at 12:00
learninglearning
346
346
add a comment |
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%2f3017065%2freduced-complexity-of-matrix-inversion-of-sum-of-rank-1-matrices-m-1-lef%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%2f3017065%2freduced-complexity-of-matrix-inversion-of-sum-of-rank-1-matrices-m-1-lef%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
