# Questions tagged [least-squares]

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### 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 ...
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### 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 ...
43 views

### Spline interpolation for vector-valued data in 3D space

I have output from a 3D linear elasticity finite element simulation which uses linear tetrahedral elements, such that the displacement is continuous over the nodes but the gradient is not ($C_0$ ...
60 views

### How applying the gradient descent method for solving a least square problem can remove the blur from an image?

I got an assignment where it asked to implement (in MATLAB) the gradient descent algorithm in order to resolve an ill posed least square problem: $$\min_u \Vert Gu - f \Vert$$ where $u$ is the ...
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### How to model a non-linear least-squares problem for triangles

I have a non-linear least-squares problem to solve and with my current modeling the solver is either very slow or does not converge to a correct solution. For the problem I need to minimize an energy ...
35 views

### fitting exponential versus exponential w/ power

I have two models which I would like to investigate for my data. One form is: $$\label{one} f(r) = A e^{-B r}$$ and the second is: \label{two} g(r)...
74 views

### Stable Method of orthogonal projection onto a subspace with the help of Moore-Penrose inverse,

Projection of a vector $v$ onto the column space of a matrix $A$ is given by $AA^\dagger v$. From the definition of Moore-Penrose Inverse we know that $AA^\dagger v = (A^T)^\dagger A^T v$. Below is ...
61 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: I'...
63 views

### 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 ...
212 views

### Update for QR factorization least squares

I found after some research that the most numerically stable way to solve the least squares problem is through QR factorization. For $n$ number of observations and $p$ number of parameters it takes ...
119 views

### How can we solve the normal equations with limited memory?

I was asked this open ended question in an interview once: How would you find a solution to the normal equations with limited memory? Unlike Solving sparse least squares system with limited memory, ...
405 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 ...
I would like to create an optimization solution for black-box software calculations. Currently, I am using the Levenberg-Marquardt algorithm to update a vector of parameters, $\beta$, with residuals, \$...