# Questions tagged [least-squares]

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### Reweighted least squares factorization

This is a continuation of the question asked here. I want to solve numerous least squares systems of the form $$D_i A x \approx D_i b$$ where $D_i$ are $m \times m$ diagonal matrices with positive ...
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### Purely rotational least squares match

Could anyone recommend a method for the following least-squares problem: find $R \in \mathbb{R}^{3 \times 3}$ that minimizes: $\sum\limits_{i=0}^N (Rx_i - b_i)^2 \rightarrow \min$, where $R$ is a ...
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### Nonlinear least-squares solvers vs. generic minimization

A nonlinear least-squares problem with $F:\mathbb{R}^m\to\mathbb{R}^n$, $$F(x) \to \min_x \quad (\text{in the least-squares sense})$$ really means minimizing $$\frac{1}{2} \|F(x)\|^2 \to \min_x.$$ ...
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### fitting exponential versus exponential w/ power

I have two models which I would like to investigate for my data. One form is: \begin{equation} \label{one} f(r) = A e^{-B r} \end{equation} and the second is: \begin{equation} \label{two} g(r)...
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### Matlab interface for minpack2

Is there a Matlab interface for minpack2? minpack2 http://ftp.mcs.anl.gov/pub/MINPACK-2 consists of Fortran programs , but i would like to call the test problems from matlab. What can i do ?
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### Finding parameters numerically

I suspect that a function $f(x,y)$ is of the form $f(x,y)=a(bx+c)^{dy+e}$. I have access to several values of $f(x,y)$. How do I proceed numerically to find the parameters $\{a,b,c,d,e\}$? By ...
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### Solving for $C$ in $Q = YCZ$ using least squares in Matlab

I am trying to solve for the matrix $C$ in $Q = YCZ$ in matlab. I have preliminary results but they don't seem realistic. Here, $Q$ is $n \times m-1$, $Y$ is $n \times p$, $C$ is $p \times m$ and $Z$ ...
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### Least Squares and Fourier Series

I have a little bit of problem figuring out the relation between Fourier series and Least Squares. As far as I understand, LS is a way of minimizing the quadratic error between a measured value $y_i$ ...
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### Solve ill-posed linear system without transposing matrices?

I am attempting to use an iterative solver to solve $p$ in $$Jp = -r$$ where $J$ is an $m\times m$ matrix. Unfortunately, this is an ill-posed problem and possibly infinite versions of $p$ exist. ...
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### Description of algorithm for small scale linear least squares with box constraints

I have small scale dense least squares problem with box constraints $$\mbox{argmin}||Ax - b||^2 \quad$$ $$\mbox{subject to} \quad l_i \leq x_i \leq u_i,$$ Number of variables is about 10-50, ...
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### Solving multiple least-square problems with the same constraints

The following least-square problem can be solved efficiently (e.g. using matlab's lsqlin): $$\vec{x}^*=\arg\min_\vec{x} ||C\vec{x}-\vec{t}||^2\,\ s.t.\ Ax \le \vec{b}$$ where the parameters of the ...
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### Optimisation of purely integer quantity with bound-constraints for a 1D expensive function whose analytical form is not available

I have a computationally expensive objective function, whose analytical form is not available. The only input argument to the objective function is an integer variable. The goal is to compute the ...
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