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1answer
59 views

Least Angle when $\textbf{A}^T\textbf{A}$ is singular

I'm teaching myself this regression stuff, so forgive me if this is a basic question. I can't seem to find a discussion of my particular problem. So I'm least-squares-ing this overdetermined system ...
8
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3answers
190 views

Least squares approximation question

I am taking a course on scientific computation, and we just went over least squares approximation. My question is specifically about approximating using polynomials. I understand that if you have n+1 ...
3
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1answer
53 views

Does the covariance matrix in Least Squares depend upon the input data?

I had always assumed that the covariance matrix depends upon the amount and quality of your input data, but I am finding out that this is not the case. Is this true? We want to fit $f(t) = ...
2
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1answer
107 views

Solve Regularized Least Squares problems using Matlab optimization toolbox

I am trying to solve a least squares problem where the objective function has a least squares term along with L1 and L2 norm regularization. I am unable to find which matlab function provides the ...
3
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1answer
45 views

Large-scale box-constrained linear least-squares

I need to solve $$\mbox{min}||Ax - b||_2^2 \quad \mbox{s.t.} \quad l \leq x \leq u,$$ where $A \in R^{m \times n}$, $m \ll n$, $n \approx 10^4-10^5$. BVLS [1] based on active-set method works fine ...
1
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1answer
53 views

How can I reuse the SVD of matrix A to solve LS problems for both A and its transpose via Eigen C++?

If $A\in R^{m\times n}, b\in R^m, c\in R^n$, if I need to solve the least square problems via SVD of $A$ and $A^T$, i.e. I need to solve the least square solutions to following linear systems via ...
9
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1answer
114 views

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 : $\sum_{i=0}^N (Rx_i - b_i)^2 \rightarrow min$, where $R$ is unitary ...
0
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1answer
68 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 ...
4
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1answer
112 views

Factorization for reweighted least squares

I am solving a problem using an iteratively-reweighted least squares method: http://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares Essentially this requires solving a number of ...
3
votes
1answer
79 views

indirect method for least-squares with inequality constraints

I aim to find $x \in \mathbb{R}^n$ that $\min_x |D \cdot F \cdot x|^2$ subject to $x_i = X_i$ and $x_j \geq X_j$ , $i \in I, j \in J$ and I and J partition ${1\cdots N}$ into two sets. it is ...
2
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2answers
137 views

Solving non-negative least squares in Matlab (by analogy with least squares)

There is a least-squares problem. It can be solved using backslash in Matlab. If Ax = b, then x = A \ b. Let's assume that I ...
1
vote
1answer
99 views

FETI-DP or BDDC with least squares FEM?

Have FETI-DP or BDDC methods been applied to alternative FEM discretizations - for example, least squares finite elements? My Google searching doesn't seem to yield many results, so I'm wondering if ...
6
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2answers
177 views

Proving convergence of adaptive finite elements - min res FEM?

There's a body of work out there dealing with the discrete convergence of adaptive finite element methods using error estimators. Most deal with proving the property $\|u-u_{k+1}\|_U \leq (1-\alpha) ...
5
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0answers
175 views

Using MINPACK for curve fitting: implementation?

I need to implement a non-linear fitting algorithm in Fortran and chose to use MINPACK's flavor of the Levenberg-Marquardt algorithm as a basis for the least-squares stuff. However, I seem to ...
0
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1answer
126 views

SVD regularization - ray 2D tomography

Sunny day today, isn't it? Please, I need help with my problem. I have written a program to do 2D ray tomography, according to this paper. For the result, I use formula (4.15) from the paper. Now I ...
3
votes
1answer
135 views

Fitting one set of points to another by a rigid motion

I'm not really sure how to explain this problem clearly, so please bear with me. I have a basis of 3 orthonormal unit vectors and a position, a standard 4x4 transform matrix in computer graphics. ...
4
votes
2answers
216 views

Complex least-squares problem

Having a matrix $\mathbf{A} \in \mathcal{C}^{m\times n}$ I solve following least-squares problem $$Re(\mathbf{A}^H \mathbf{A})x=Re(\mathbf{A}^H\mathbf{b}).$$ If the matrix $\mathbf{A}$ was a real ...
6
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4answers
564 views

parameters estimation

I have to estimate a parameter (K), but I don't know how I can do it. I think by a regression model (minimum least square?), but I'm not sure. The system is: ...
3
votes
1answer
124 views

How do you formulate the linear least-squares method for radiometric calibration?

In Debevec and Malik (mentioned similarly in Forsyth and Ponce's Computer Vision: A Modern Approach) they highlight a method of solving the camera response function using linear least-squares. We ...
1
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1answer
3k views

MATLAB Code Evaluation for Least Squares Regression (LSR) [closed]

Below is my own approach to implement the Least Squares Regression algorithm in MATLAB. Could you please take a look and tell me if it makes sense; if it does exactly what is supposed to do? EDIT: ...
5
votes
3answers
266 views

How to solve a small least-squares problem

This question is not very deep. Suppose I have a small rectangular matrix $A$, with number of rows and columns between $50$-$100$, respectively. Given a right-hand side $b$, I want to solve the ...
7
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2answers
803 views

Solving a least squares problem with linear constraints in Python

I need to solve \begin{alignat}{1} & \min_{x}\|Ax - b\|^2_{2}, \\ \mathrm{s.t.} & \quad\sum_{i}x_{i} = 1, \\ & \quad x_{i} \geq 0, \quad \forall{i}. \end{alignat} I think it is a ...
10
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2answers
716 views

Newton-based methods in optimization vs. solving systems of nonlinear equations

I asked for clarification about a recent question about minpack, and got the following comment: Any system of equations is equivalent to an optimization problem, which is why Newton-based methods ...