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2
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1answer
49 views

Minimizing Cost Functions using Iterative Least Squares

I am currently trying to use iterative least squares to solve a system, $y = Hx + v$ where $y$ is a vector of observations, $H$ is the design matrix, and $v$ is the observation error. From my ...
0
votes
0answers
20 views

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 ?
2
votes
0answers
39 views

Calculating theoretical order of accuracy of least squares fit advection scheme

I'm familiar with finding the order of accuracy using von Neumann analysis for finite difference schemes formulated using Taylor series expansions. But is there a similar technique for finding the ...
2
votes
0answers
32 views

Fortran solver for the Sparse LSE problem

I was wondering if there is a Fortran library that contains a solver for the Sparse LSE(linear equality-constrained least squares) problem $$ min_{x}\|Cx-d\|^2 \text{ subject to } Ax=b $$ where $A$ ...
1
vote
1answer
57 views

Least Square fit with Double Zernike Polynomials

I need to describe the optical aberrations of my set-up with Zernike polynomials. To do this, I want to fit the first 15 polynomials in the following way on my data: $$\chi^2 = \sum_k\left(\beta_k^x ...
2
votes
1answer
66 views

Projecting onto convex shapes - best fit convex polygon

I am interested in studying a problem of the form $\min F(\Omega)$ where $\Omega$ varies in the class of convex, open sets in the plane. An idea is to deform $\Omega$ at each step using a steepest ...
1
vote
0answers
31 views

linear solution of curve fitting on multiple linear functions differing by a multiplier

I am facing the following problem. I know nonlinear least squares can provide a solution but I am wondering if a linear way to solve this data fitting problem may exists. This is my input dataset: ...
1
vote
3answers
113 views

rank-deficient NNLS

I want to find the minimum-norm solution to a rank-deficient least-squares problem, subject to positivity constraints, e.g. $$\min_x\ \|x\|^2 \quad s.t.\quad Ax = b,\ x \geq 0$$ where $A$ is large, ...
2
votes
0answers
230 views

Polynomial Fitting with Least Squares using Numpy and Scipy

I am trying to fit data to a polynomial using Python - Numpy. The points, with lines sketched above them are as in the picture. I am trying to fit those points to a polynomial of 4. or 5. degree. ...
3
votes
2answers
685 views

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 $y_i$ ...
3
votes
1answer
347 views

solving a linearly-constrained sparse linear least-squares problem

[ question reposted from http://math.stackexchange.com/questions/786612/solving-a-linearly-constrained-sparse-linear-least-squares-problem ] Given the system of equations $Ax=b$, subject to $Cx\le ...
0
votes
1answer
64 views

Least squares fitting

I have the following equation I came across which was solved using least squares $x = \sum_{n=1}^{N} A_{n} y_{n}$ Where $x$ is a $m \times p$ matrix and $y$ would be of size $m \times p$ as well ...
1
vote
1answer
65 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 ...
9
votes
3answers
472 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 ...
4
votes
1answer
67 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
votes
1answer
269 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
votes
1answer
109 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
vote
1answer
291 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
votes
1answer
255 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
votes
1answer
120 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
votes
1answer
132 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
206 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
votes
2answers
568 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
138 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
votes
2answers
206 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) ...
4
votes
0answers
554 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
votes
1answer
179 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
519 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
335 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
votes
4answers
928 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
148 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
vote
1answer
5k 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
318 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
votes
2answers
1k 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 ...
11
votes
2answers
1k 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 ...