Nonlinear least squares with analytical solution
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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 Nov 19 at 10:02
MrYouMath
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up vote
1
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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 Nov 19 at 10:02
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 Nov 19 at 10:02
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 Nov 19 at 10:02
MrYouMath
13.8k31236
asked Nov 19 at 10:02
MrYouMath
13.8k31236
asked Nov 19 at 10:02
MrYouMath
13.8k31236
asked Nov 19 at 10:02
MrYouMath
13.8k31236
asked Nov 19 at 10:02
MrYouMath
13.8k31236
13.8k31236
add a comment |
add a comment |
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