For n = 2 … 11 set up Vandermonde matrix A of size m × n and for each n given data set a. Matlab
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box;
}
I am given set of 50 data points with values {a^(i),b^(i)} for i=1,...,50
stored in the arrays a and b.
I know that the Vandermonde matrix A has size m x n, where n = 2 ... 11 and m is the size of the array a.
I want to to fit the data with a polynomial of degree (n − 1), for n = 2,...,11. To do that for each n I have to set up the Vandermonde matrix A of size m × n.
The Vandermonde matrix A solves the following equation:
A^T*A*x = A^T*b
Where the A^T is the transpose matrix and I have b already given.
Also we know that Aij = (a^(i))^(j−1) for j = 1,...,n,
What confuses me is how to set the matrix for n = 2,..,11.
What my line of thought is:
I have m = length(a); this will set up m = 50;
n = 11;
Then A=ones(m,n); This creates a matrix A filled with ones that has the correct size.
However I am not sure how to populate the matrix.
I wrote the following for loop which I thought will populate the matrix:
for n = 2:11
j=n;
for i = 1:50
A(i,n) = (a^(i))^(j-1);
end
end
Could you help me please with setting up the matrix?
matlab matrix
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
add a comment |
I am given set of 50 data points with values {a^(i),b^(i)} for i=1,...,50
stored in the arrays a and b.
I know that the Vandermonde matrix A has size m x n, where n = 2 ... 11 and m is the size of the array a.
I want to to fit the data with a polynomial of degree (n − 1), for n = 2,...,11. To do that for each n I have to set up the Vandermonde matrix A of size m × n.
The Vandermonde matrix A solves the following equation:
A^T*A*x = A^T*b
Where the A^T is the transpose matrix and I have b already given.
Also we know that Aij = (a^(i))^(j−1) for j = 1,...,n,
What confuses me is how to set the matrix for n = 2,..,11.
What my line of thought is:
I have m = length(a); this will set up m = 50;
n = 11;
Then A=ones(m,n); This creates a matrix A filled with ones that has the correct size.
However I am not sure how to populate the matrix.
I wrote the following for loop which I thought will populate the matrix:
for n = 2:11
j=n;
for i = 1:50
A(i,n) = (a^(i))^(j-1);
end
end
Could you help me please with setting up the matrix?
matlab matrix
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
add a comment |
I am given set of 50 data points with values {a^(i),b^(i)} for i=1,...,50
stored in the arrays a and b.
I know that the Vandermonde matrix A has size m x n, where n = 2 ... 11 and m is the size of the array a.
I want to to fit the data with a polynomial of degree (n − 1), for n = 2,...,11. To do that for each n I have to set up the Vandermonde matrix A of size m × n.
The Vandermonde matrix A solves the following equation:
A^T*A*x = A^T*b
Where the A^T is the transpose matrix and I have b already given.
Also we know that Aij = (a^(i))^(j−1) for j = 1,...,n,
What confuses me is how to set the matrix for n = 2,..,11.
What my line of thought is:
I have m = length(a); this will set up m = 50;
n = 11;
Then A=ones(m,n); This creates a matrix A filled with ones that has the correct size.
However I am not sure how to populate the matrix.
I wrote the following for loop which I thought will populate the matrix:
for n = 2:11
j=n;
for i = 1:50
A(i,n) = (a^(i))^(j-1);
end
end
Could you help me please with setting up the matrix?
matlab matrix
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
I am given set of 50 data points with values {a^(i),b^(i)} for i=1,...,50
stored in the arrays a and b.
I know that the Vandermonde matrix A has size m x n, where n = 2 ... 11 and m is the size of the array a.
I want to to fit the data with a polynomial of degree (n − 1), for n = 2,...,11. To do that for each n I have to set up the Vandermonde matrix A of size m × n.
The Vandermonde matrix A solves the following equation:
A^T*A*x = A^T*b
Where the A^T is the transpose matrix and I have b already given.
Also we know that Aij = (a^(i))^(j−1) for j = 1,...,n,
What confuses me is how to set the matrix for n = 2,..,11.
What my line of thought is:
I have m = length(a); this will set up m = 50;
n = 11;
Then A=ones(m,n); This creates a matrix A filled with ones that has the correct size.
However I am not sure how to populate the matrix.
I wrote the following for loop which I thought will populate the matrix:
for n = 2:11
j=n;
for i = 1:50
A(i,n) = (a^(i))^(j-1);
end
end
Could you help me please with setting up the matrix?
matlab matrix
matlab matrix
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
asked Nov 26 '18 at 22:27
Lachezar PetkovLachezar Petkov
1
1
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
You should use the vander function. However, vander will return an m x m matrix, which is usually used to fit the data to a polynomial of degree (m-1). Since you want to fit to a polynomial of degree (n-1), you only need the last n columns of that matrix.
Here's the code:
A = vander(a);
A = A(:,end-n+1:end);
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "1"
};
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
},
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%2fstackoverflow.com%2fquestions%2f53490070%2ffor-n-2-11-set-up-vandermonde-matrix-a-of-size-m-%25c3%2597-n-and-for-each-n-given%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You should use the vander function. However, vander will return an m x m matrix, which is usually used to fit the data to a polynomial of degree (m-1). Since you want to fit to a polynomial of degree (n-1), you only need the last n columns of that matrix.
Here's the code:
A = vander(a);
A = A(:,end-n+1:end);
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
add a comment |
You should use the vander function. However, vander will return an m x m matrix, which is usually used to fit the data to a polynomial of degree (m-1). Since you want to fit to a polynomial of degree (n-1), you only need the last n columns of that matrix.
Here's the code:
A = vander(a);
A = A(:,end-n+1:end);
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
add a comment |
You should use the vander function. However, vander will return an m x m matrix, which is usually used to fit the data to a polynomial of degree (m-1). Since you want to fit to a polynomial of degree (n-1), you only need the last n columns of that matrix.
Here's the code:
A = vander(a);
A = A(:,end-n+1:end);
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
You should use the vander function. However, vander will return an m x m matrix, which is usually used to fit the data to a polynomial of degree (m-1). Since you want to fit to a polynomial of degree (n-1), you only need the last n columns of that matrix.
Here's the code:
A = vander(a);
A = A(:,end-n+1:end);
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
edited Nov 27 '18 at 3:12
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
answered Nov 27 '18 at 0:44
SavithruSavithru
592511
592511
add a comment |
add a comment |
Thanks for contributing an answer to Stack Overflow!
- 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%2fstackoverflow.com%2fquestions%2f53490070%2ffor-n-2-11-set-up-vandermonde-matrix-a-of-size-m-%25c3%2597-n-and-for-each-n-given%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
