Nonlinear least squares with analytical solution
up vote
1
down vote
favorite
I want to find a "true" nonlinear least squares problem which does have an analytical solution.
I tried to construct something with a Dirac-Delta function and ended up with $y_n = c^2delta(x_n-x_1)x_n+varepsilon_n$, in which I assumed a dataset $mathcal{D}=left{(x_1,y_1),ldots,(x_N,y_N) right}$. This equation is not really nonlinear in the coefficients as we can reformulate the regression equation to $y_n=tilde{c}delta(x_n-x_1)x_n+varepsilon_n$ with $tilde{c}geq 0$, hence this would still count as a linear regression with nonlinear basis functions.
Is there a well-known example of a nonlinear least squares problem that does have an analytical closed-form solution? References are appreciated.
closed-form least-squares
asked 19 hours ago
MrYouMath
13.8k31236
add a comment |
up vote
1
down vote
favorite
I want to find a "true" nonlinear least squares problem which does have an analytical solution.
I tried to construct something with a Dirac-Delta function and ended up with $y_n = c^2delta(x_n-x_1)x_n+varepsilon_n$, in which I assumed a dataset $mathcal{D}=left{(x_1,y_1),ldots,(x_N,y_N) right}$. This equation is not really nonlinear in the coefficients as we can reformulate the regression equation to $y_n=tilde{c}delta(x_n-x_1)x_n+varepsilon_n$ with $tilde{c}geq 0$, hence this would still count as a linear regression with nonlinear basis functions.
Is there a well-known example of a nonlinear least squares problem that does have an analytical closed-form solution? References are appreciated.
closed-form least-squares
asked 19 hours ago
MrYouMath
13.8k31236
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I want to find a "true" nonlinear least squares problem which does have an analytical solution.
I tried to construct something with a Dirac-Delta function and ended up with $y_n = c^2delta(x_n-x_1)x_n+varepsilon_n$, in which I assumed a dataset $mathcal{D}=left{(x_1,y_1),ldots,(x_N,y_N) right}$. This equation is not really nonlinear in the coefficients as we can reformulate the regression equation to $y_n=tilde{c}delta(x_n-x_1)x_n+varepsilon_n$ with $tilde{c}geq 0$, hence this would still count as a linear regression with nonlinear basis functions.
Is there a well-known example of a nonlinear least squares problem that does have an analytical closed-form solution? References are appreciated.
closed-form least-squares
asked 19 hours ago
MrYouMath
13.8k31236
I want to find a "true" nonlinear least squares problem which does have an analytical solution.
I tried to construct something with a Dirac-Delta function and ended up with $y_n = c^2delta(x_n-x_1)x_n+varepsilon_n$, in which I assumed a dataset $mathcal{D}=left{(x_1,y_1),ldots,(x_N,y_N) right}$. This equation is not really nonlinear in the coefficients as we can reformulate the regression equation to $y_n=tilde{c}delta(x_n-x_1)x_n+varepsilon_n$ with $tilde{c}geq 0$, hence this would still count as a linear regression with nonlinear basis functions.
Is there a well-known example of a nonlinear least squares problem that does have an analytical closed-form solution? References are appreciated.
closed-form least-squares
closed-form least-squares
asked 19 hours ago
MrYouMath
13.8k31236
asked 19 hours ago
MrYouMath
13.8k31236
asked 19 hours ago
MrYouMath
13.8k31236
asked 19 hours ago
MrYouMath
13.8k31236
asked 19 hours ago
MrYouMath
13.8k31236
13.8k31236
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3004734%2fnonlinear-least-squares-with-analytical-solution%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
