From trilinear interpolation to linear interpolation.
$begingroup$
I have trouble understanding the following:
Let us assume that we have some $Omega()$ data generating process, which generates {$h,x,y,z$} points. Let us assume that it is possible to construct the functional relationship of the form $h=f(x,y,z)$ by applying trilinear spline interpolation technique.
Now instead of $Omega(h,x,y,z)$ generating process let's take into consideration the following process $Omega(h,x,y^*,z^*)$, where $y^*$ and $z^*$ are scalars. Therefore we can construct $h=f(x)$ function using simple linear spline interpolation (for given values of $y,z$).
My question is the following: If we consider the following function $h=f(x,y^*,z^*)$ obtained from trilinear interpolation, does it coincide with $h=f(x)$ (for fixed $y^*,z^*$) obtained from linear spline interpolation?
approximation interpolation
asked Dec 25 '18 at 9:56
sanesane
7611
$endgroup$
add a comment |
$begingroup$
I have trouble understanding the following:
Let us assume that we have some $Omega()$ data generating process, which generates {$h,x,y,z$} points. Let us assume that it is possible to construct the functional relationship of the form $h=f(x,y,z)$ by applying trilinear spline interpolation technique.
Now instead of $Omega(h,x,y,z)$ generating process let's take into consideration the following process $Omega(h,x,y^*,z^*)$, where $y^*$ and $z^*$ are scalars. Therefore we can construct $h=f(x)$ function using simple linear spline interpolation (for given values of $y,z$).
My question is the following: If we consider the following function $h=f(x,y^*,z^*)$ obtained from trilinear interpolation, does it coincide with $h=f(x)$ (for fixed $y^*,z^*$) obtained from linear spline interpolation?
approximation interpolation
asked Dec 25 '18 at 9:56
sanesane
7611
$endgroup$
add a comment |
$begingroup$
I have trouble understanding the following:
Let us assume that we have some $Omega()$ data generating process, which generates {$h,x,y,z$} points. Let us assume that it is possible to construct the functional relationship of the form $h=f(x,y,z)$ by applying trilinear spline interpolation technique.
Now instead of $Omega(h,x,y,z)$ generating process let's take into consideration the following process $Omega(h,x,y^*,z^*)$, where $y^*$ and $z^*$ are scalars. Therefore we can construct $h=f(x)$ function using simple linear spline interpolation (for given values of $y,z$).
My question is the following: If we consider the following function $h=f(x,y^*,z^*)$ obtained from trilinear interpolation, does it coincide with $h=f(x)$ (for fixed $y^*,z^*$) obtained from linear spline interpolation?
approximation interpolation
asked Dec 25 '18 at 9:56
sanesane
7611
$endgroup$
I have trouble understanding the following:
Let us assume that we have some $Omega()$ data generating process, which generates {$h,x,y,z$} points. Let us assume that it is possible to construct the functional relationship of the form $h=f(x,y,z)$ by applying trilinear spline interpolation technique.
Now instead of $Omega(h,x,y,z)$ generating process let's take into consideration the following process $Omega(h,x,y^*,z^*)$, where $y^*$ and $z^*$ are scalars. Therefore we can construct $h=f(x)$ function using simple linear spline interpolation (for given values of $y,z$).
My question is the following: If we consider the following function $h=f(x,y^*,z^*)$ obtained from trilinear interpolation, does it coincide with $h=f(x)$ (for fixed $y^*,z^*$) obtained from linear spline interpolation?
approximation interpolation
approximation interpolation
asked Dec 25 '18 at 9:56
sanesane
7611
asked Dec 25 '18 at 9:56
sanesane
7611
edited Dec 25 '18 at 12:57
sane
asked Dec 25 '18 at 9:56
sanesane
7611
asked Dec 25 '18 at 9:56
sanesane
7611
asked Dec 25 '18 at 9:56
sanesane
7611
7611
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
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%2f3051983%2ffrom-trilinear-interpolation-to-linear-interpolation%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%2f3051983%2ffrom-trilinear-interpolation-to-linear-interpolation%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
