Numerical Change of Variables
If I have $f(x)$ represented by 2 arrays. One array is the arrays of $x$ while the other is output from $f(x)$. So basically a numerical representation of the function. If I don't know what $f(x)$ is, can I still change the variable. For example can I calculate $f(frac{1}{x})$ from what I know.
numerical-methods change-of-variable numerical-calculus
asked Nov 29 '18 at 20:29
twofairtwofair
103
add a comment |
If I have $f(x)$ represented by 2 arrays. One array is the arrays of $x$ while the other is output from $f(x)$. So basically a numerical representation of the function. If I don't know what $f(x)$ is, can I still change the variable. For example can I calculate $f(frac{1}{x})$ from what I know.
numerical-methods change-of-variable numerical-calculus
asked Nov 29 '18 at 20:29
twofairtwofair
103
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35
add a comment |
If I have $f(x)$ represented by 2 arrays. One array is the arrays of $x$ while the other is output from $f(x)$. So basically a numerical representation of the function. If I don't know what $f(x)$ is, can I still change the variable. For example can I calculate $f(frac{1}{x})$ from what I know.
numerical-methods change-of-variable numerical-calculus
asked Nov 29 '18 at 20:29
twofairtwofair
103
If I have $f(x)$ represented by 2 arrays. One array is the arrays of $x$ while the other is output from $f(x)$. So basically a numerical representation of the function. If I don't know what $f(x)$ is, can I still change the variable. For example can I calculate $f(frac{1}{x})$ from what I know.
numerical-methods change-of-variable numerical-calculus
numerical-methods change-of-variable numerical-calculus
asked Nov 29 '18 at 20:29
twofairtwofair
103
asked Nov 29 '18 at 20:29
twofairtwofair
103
asked Nov 29 '18 at 20:29
twofairtwofair
103
asked Nov 29 '18 at 20:29
twofairtwofair
103
asked Nov 29 '18 at 20:29
twofairtwofair
103
103
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35
add a comment |
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35
add a comment |
1 Answer
1
active
oldest
votes
Let's say that you know $f(x_i)=f_i$ for $i=1,dots,n$. Consider the function $g(x)=f(1/x)$ and the points $y_i=1/x_i$. Then you know $g(y_i)=f_i$. Now you can use any quadrature rule (for instance the trapezoidal rule) to get an estimate of the integral of $g$.
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
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%2f3019162%2fnumerical-change-of-variables%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
Let's say that you know $f(x_i)=f_i$ for $i=1,dots,n$. Consider the function $g(x)=f(1/x)$ and the points $y_i=1/x_i$. Then you know $g(y_i)=f_i$. Now you can use any quadrature rule (for instance the trapezoidal rule) to get an estimate of the integral of $g$.
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
add a comment |
Let's say that you know $f(x_i)=f_i$ for $i=1,dots,n$. Consider the function $g(x)=f(1/x)$ and the points $y_i=1/x_i$. Then you know $g(y_i)=f_i$. Now you can use any quadrature rule (for instance the trapezoidal rule) to get an estimate of the integral of $g$.
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
add a comment |
Let's say that you know $f(x_i)=f_i$ for $i=1,dots,n$. Consider the function $g(x)=f(1/x)$ and the points $y_i=1/x_i$. Then you know $g(y_i)=f_i$. Now you can use any quadrature rule (for instance the trapezoidal rule) to get an estimate of the integral of $g$.
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
Let's say that you know $f(x_i)=f_i$ for $i=1,dots,n$. Consider the function $g(x)=f(1/x)$ and the points $y_i=1/x_i$. Then you know $g(y_i)=f_i$. Now you can use any quadrature rule (for instance the trapezoidal rule) to get an estimate of the integral of $g$.
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
answered Nov 29 '18 at 20:38
FedericoFederico
4,849514
4,849514
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
add a comment |
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
Thanks, you are correct. It makes sense. I think I was working on this problem for too long and got lost in some details. Thanks again
– twofair
Nov 30 '18 at 21:06
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.
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%2f3019162%2fnumerical-change-of-variables%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
Well, you know the values of $f(1/x)$ at the sampled points $1/x_i$, so you can use a quadrature formula to have an estimate of the integral. No need to "change the variable"
– Federico
Nov 29 '18 at 20:35