Questions tagged [least-squares]

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How to code gradient descent-based Tikhonov denoising that exactly matches LSQ Tikhonov denoise?

(Note: Corrected code is posted below the original code.) For an exercise in optimization, I am interested in coding a simple example from scratch: a Tikhonov denoising routine using gradient descent,...
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1answer
113 views

Using least squares for computing gradients

I am developing a code where I am using the least squares method to compute gradients. Generally, we use least squares to obtain some model based on a set of data (${q_1 \cdots q_N}$) at locations ($...
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1answer
201 views

How to recover the 3x4 pinhole camera from 9 parameters

I downloaded the bundle adjustment data from this link: original data for bundle adjustment which is the supporting data for a paper titled: Bundle Adjustment in the Large I want to use the data ...
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Blown-up iterates in Gauss-Newton method

I am working on a non-linear least squares problem with standard form, in which I need to calibrate a parameter vector $\Theta$ to a set of inputs $\mathbf{x}$ and outputs $\mathbf{y}$: $$\begin{align}...
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Implementation method selection for sparse constrained linear least squares or quadratic programming

I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints. I have ...
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1answer
282 views

How to use LAPACK function (DGELSY) in Fortran

I am trying to use Least Squares Minimization to solve a the matrix problem: b = A*x for x. The system is overdetermined, and A is a dense matrix. In the LAPACK library, I believe the routine DGELSY ...
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106 views

Parameter estimation using fmincon

This is a follow up to my previous question posted here. I am solving an optimization problem using fmincon in MATLAB. There are no equality constraints in my model....
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243 views

computation complexity of OLS in estimating a VAR model

Could someone tell me the computation cost of using Ordinary least squares in estimating a Vector autoregression model? I am thinking the cost is O(n) where n is the number of the training instance. ...
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1answer
33 views

Minimize squared error of linear function

Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the ...
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1answer
38 views

Trouble Estimating Motor Parameters with Least Squares in MATLAB

Basically, I'm trying to use Least-Squares to estimate the parameters of a DC motor. My system can be modeled by the following matrix equation: $$\begin{bmatrix}V_{input}(t)\\0\end{bmatrix}=\begin{...

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