Nonlinear Least Squares Minimization

swartzism
Messages
103
Reaction score
0
How should I go about solving this problem? This is only to get a better understanding of how NLLS works.

F(x;a) = (1+a1*x)/(a2+a3*x) (so n = 3)

I am choosing a1,a2,a3 to be 2,3,5 respectively. I am also picking 6 data points (so m = 6):

(0, 0), (-1/4, 1/4), (-1/2, 1/10), (1/4, 1/4), (1, 1), (1/2, 1/2).

I'm not even sure where to begin to attack this problem.

Any suggestions?
 
Physics news on Phys.org
The Levenberg-Marquardt algorithm is a widely used method.

Alternatively, you can treat NLLSQ as a general nonlinear optimization problem, and use standard optimization methods like the BFGS algorithm if the problem is fairly well behaved, or the simplex search method (which can be very slow, but will find a local minimum of pretty much anything!) if it isn't.

IIRC all these are in "Numerical Recipes", or Google for other explanations of the algorithms and computer code.
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

MHB Bilinear transformation not working
Replies
5
Views
2K
A Anti-dual numbers and what are their properties?
Replies
1
Views
2K
Comp Sci An Introduction to Deep Learning and Modifying Code
Replies
7
Views
1K
Reproduce band structure Kagome Fermi-Hubbard using Python
Replies
6
Views
2K
Determine if vector b is a linear combination of vectors a1, a2, a3.
Replies
7
Views
6K
I Trouble understanding an online solution to an exercise in Dummit & Foote
Replies
2
Views
574
I Definition of minimal ideal using symbolic logic notation
Replies
3
Views
548
A Have I solved this iterative equation correctly?
Replies
2
Views
200
A discrete-time queue Markov Chain problem
Replies
12
Views
2K
I Dfns group action & group, written in terms of the other
Replies
26
Views
370

Hot Threads

Recent Insights

Back
Top