# Tag Info

• 17.6k
Accepted

### Finding rate of convergence by curve fitting in Matlab

First of all, rates of convergence are usually given in the form $$\|u-u_h\| \leq C N^\alpha,$$ rather than equality. Furthermore, rates are asymptotic, i.e., only have to hold for $N\to \infty$. ...
• 11.9k
Accepted

### Fitting Implicit Surfaces to Oriented Point Sets

I was surprised for not receiving a satisfactory answer to the question above and my investigations showed me that this, indeed is an unexplored area. Hence, I put some effort in developing solutions ...
• 2,139

### Curve fitting for oscillating data

Numerical judgement of model choice: You model 36 observations with a model consisting of 12 or 13 predictor variables. This is most likely not a good model. Even if you reach a high $R^2_{adj}$, you ...

• 3,673
Accepted

### Constrained linear least squares matrix equation

This is a constrained minimization problem (with linear constraints). You can write it like $$\min_X \frac{1}{2}\|AX-B\|^2_2 \quad \text{ s.t. } e^TX = 1$$ where $e$ is the vector of all ones. ...
• 2,961
Accepted

### How do I correctly multiply vectors and matrices in Python and MATLAB?

David Ketcheson has already indicated the problem in his comment. I will flesh it out here. Note the form of the argument of the log in the logistic regression objective: $log[1+exp(−b_iA^T_ix)]$ ...
• 656

### Seeking a free symbolic regression software

I found the gramEvol R package flexible and easy to use. They have a small tutorial in which they rederive Kepler's third law from data. Note that it relies on Genetic Programmic for its optimisation ...

### What equation should I fit this set of data points to?

An assortment of curves for fitting chemistry examples is presented in these Colby College class notes. Of particular application is the sigmoid response curve with variable "slope" for the central ...
• 3,189

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

That might also have been a trick question. Let's say you want to solve the normal equations for $Ax=b$, i.e., $(A^T A) x = A^T b$. Let's assume for a moment that the questioner meant that $A$ is ...
• 50.2k

If my computer history is not wrong, no one would use the initial guess obtained from the quadratic polynomial you provided and use the algorithm you suggested. This is due to two reasons: floating-...
• 2,291

This polynomial $p(x)$ solves the minimax optimization for $$\frac{p(x)}{\sqrt{x}}-1$$ over the interval $[\tfrac12,1]$.
• 131
Accepted

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

Minimizing the 2-norm of $x$ among all least squares solutions is relatively easy to do- this is the pseudoinverse solution. It can be computed using either a rank revealing version of the QR ...
• 17.6k

### Seeking a free symbolic regression software

There is also a package for R called rgp. Visit this link. https://cran.r-project.org/web/packages/rgp/index.html I have not used rgp as I have only begun to use R seriously but it seemed like a ...
• 21

### What are good parametrizations of rational functions for response surface models?

What are good parametrizations of rational functions for response surface models? A widely used flexible parametrization of (piecewise) rational functions are non-uniform rational basis spline (NURBS)...
• 2,121

### Fitting 2D mapping data from multiple measurements

If you know that you have $n$ points $X_1,...,X_n$ and the desired pairwise distances $d_{ij}$ between $X_i$ and $X_j$ you could try and optimize the functional $$\sum_{i<j} (d_{ij}-|X_i-X_j|)^2$$ ...
• 965
Accepted

• 7,902