Comments (4)
Hi @haloinca 👋 ,
First of all, I am very sorry for not replying. For some reason, your issue went unnoticed :/
That being said, yes there is some literature to solve non-square overdetermined interval linear systems. The idea is to define an "interval least square solution" and computing it reduces to solve a symmetric (hence parametric) square interval linear system. That can be solved with e.g. the currently implemented Skalna06
solver for parametric interval linear systems, although that's probably not the most efficient ways. There should be some more optimized approaches for the symmetric case. I'll double check the literature to find a couple of relevant papers
from intervallinearalgebra.jl.
Thank you for your reply. Reading your answer, I have another question. How do I convert an "interval least square solution" into a "symmetric square interval system"? Can you explain this in more detail? Or any reference is helpful.
from intervallinearalgebra.jl.
Hi again @haloinca 👋 ,
I am very sorry for the slow follow-up, quite a busy period 😅 . As a rule of thumb, if it takes more than one week to reply, feel free to ping me even every day until you get my attention, I try to reply as fast as possible, but sometimes I get driven away by the huge amount of notifications.
Coming back to your question. In general, a golden reference for interval linear algebra is Jaroslav Horacek phd thesis, available here it is a great general overview of interval linear systems (except for the parametric case) written in a very pedagogical easy to follow way. Particularly, overdetermined systems are described in chapter 6.
Elaborating a little, given an overdetermined interval linear system
Now, this is what is generally referred as "parametric interval linear system", because the elements in the matrix (and vector) are not independent intervals, but depend on some common variables (the elements of A
). There are a few approaches to tackle this
- Forget about the dependency and treat that as a normal interval linear system. That would lead to an huge overestimation of the solution set.
- Use a parametric solver. This could be tricky because the elements of the matrix have nonlinear dependency (although there are algorithms for that).
- Use the supersquare method, that is, solve the linear system (which is equivalent to the formulation above)
This is "easier" than the previous one, because you have a linear dependency on the parameters, so could be solved e.g. with the Skalna06
method. Moreover, the thesis explores more tailored method to this specific problem.
If you have any other questions, do not hesiatate to ask, I'll try to answer quicklier next time.
Out of curiosity, do you need the overdetermined solver for a specific task? I'm asking because if this is blocking you in your work I'd be happy to bump this in my prioirity list
from intervallinearalgebra.jl.
Thank you for your patience and detailed reply, which gave me a general understanding of the interval linear system. In fact, I am a master student majoring in Electronic Engineering. I think the overdetermined solver can help me realize the interval identification problem of system parameters. I will try the methods you mentioned with the IntervalLinearAlgebra.jl toolbox.
As you may know, I am a novice to interval linear system, so there's no need to change the development plan for this impressive toolbox for my personal purposes.
from intervallinearalgebra.jl.
Related Issues (20)
- think of interface / dastructures to handle linear-PILS HOT 9
- [feature request]: FEM minimal example problem/test HOT 2
- note about adding new docs pages in cotributing guidelines.
- [enhancement]: spectral decomposition of interval matrices
- [bug] generation of documentation freezes HOT 10
- [enhancement]: Bypassing uncomputability issues HOT 1
- [enhancement]: Ship a correctly rounded threaded OpenBLAS as an Artifact HOT 1
- [enhancement]: inv and det (needed by IntervalRootFinding)
- benchmarks about different matrix multiplication algorithms HOT 2
- [bug]: issues with complex interval matrices multiplication HOT 11
- [enhancement]: format references with APA style HOT 1
- [enhancement]: Add hertz method for eigenvalues of symmetric interval matrices
- write short tutorial about eigenvalues functionalities
- TagBot trigger issue HOT 6
- video not correctly embedded in documentation HOT 3
- [bug]: don't use subset to check if interval vector is in the interior of the other HOT 2
- is the current CI an overkill HOT 1
- [enhancement]: determinant of interval matrices HOT 1
- Taking parametric interval linear system seriuosly HOT 1
Recommend Projects
-
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
-
Vue.js
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
-
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
-
TensorFlow
An Open Source Machine Learning Framework for Everyone
-
Django
The Web framework for perfectionists with deadlines.
-
Laravel
A PHP framework for web artisans
-
D3
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
-
Recommend Topics
-
javascript
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
-
web
Some thing interesting about web. New door for the world.
-
server
A server is a program made to process requests and deliver data to clients.
-
Machine learning
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
-
Visualization
Some thing interesting about visualization, use data art
-
Game
Some thing interesting about game, make everyone happy.
Recommend Org
-
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
-
Microsoft
Open source projects and samples from Microsoft.
-
Google
Google ❤️ Open Source for everyone.
-
Alibaba
Alibaba Open Source for everyone
-
D3
Data-Driven Documents codes.
-
Tencent
China tencent open source team.
from intervallinearalgebra.jl.