# Questions tagged [least-squares]

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### Symmetric linear least-squares solution

Given tall matrices $A$ and $Y$ and the following overdetermined linear system in square matrix $X$ $$AX=Y$$ is there an explicit formula for the least-squares solution if $X$ is constrained to be ...
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### How to determine the damping factor in Levenberg-Marquardt?

From the algorithm, we can see that it tries different damping factor until it gets a good one by the error. Is the damping factor related to the eigenvalues of the Hessian matrix?
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### Difference Between Total Least Squares Plane and Plane Orthogonal to Principal Axis of Inertia Tensor

Given a finite set $P$ of points in $\mathbb{E}^3$ , one can calculate an approximating plane either as the solution of a Total Least Squares problem or by interpreting the problem physically, ...
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### Minimization Proof of Conditioning on Gaussian is Gaussian

It is well known that $E[X|X+Y]$ is Gaussian if both $X$ and $Y$ are, and the result can be derived using standard density arguments. However, how can one prove it by only resulting to optimization ...
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For the Sylvester matrix equation $AX+XB=C$, I want to find the least-squares solution $X$ via $$\begin{array}{ll} \text{minimize} & \| AX + XB - C \|_{\text{F}}^2\\ \text{subject to} & \mbox{... 4 votes 1 answer 298 views ### Least square solution to AXB+CXD=E I am trying to find the least-squares solution X of the following matrix equation$$AXB+CXD=E$$Of course, I know that this equation can be written in the form$$(B^T \otimes A+D^T \otimes C) \...
I have an optimization problem of the following form $$\text{minimize} \,\|Qa-b\|_2 \quad \text{ subject to } Q \succeq 0$$ where $a,b \in \mathbb{R}^n$ are given and the $n \times n$ square matrix ...