Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Linear and Abstract Algebra
Forcing conditions in a solution of an under-determined system
Reply to thread
Message
[QUOTE="StoneTemplePython, post: 6040973, member: 613025"] Ok, there are [I]lots[/I] of ways to solve an under-determined system of equations. Two common and popular ones involve coming up with a solution vector ##\mathbf x## in your equation of ##A\mathbf x = \mathbf b##, such that ##\mathbf x## has a minimum "length" -- using a 2 norm [U]or[/U] a 1 norm. The 2 norm approach is done via typical linear algebra solvers -- but they don't accommodate the constraints you're asking about directly. (There might be an indirect workaround though it seems tedious at best and it would depend on how detailed your constraints are) On the other hand, the minimizing 1 norm approach is done via Linear Programming and is quite flexible. Supposing that the constraints you want are feasible (as in they don't preclude a feasible / valid solution), a linear programming approach can easily accommodate what you're asking for. Long story short: consider setting this up as a linear program. - - - - note: I use Julia for Linear Programming -- I've never done it in Fortran. It looks a bit dreary, but maybe something like this would be helpful for Fortran specifics: [URL]http://www.ccom.ucsd.edu/~peg/papers/sqdoc.pdf[/URL] [B]edit: [/B] for avoidance of doubt: encoding a constraint that certain parameters in your solution vector should be equal can be done via typical matrix methods and solvers. If you have a nice LP modeling setup like in Julia's JuMP, I think it's nicer to do it there, but there is nothing preventing you from tacking on new rows to the bottom of your ##A## to enforce these constraints. The real issue comes in dealing with inequality constraints like ##x_k \geq -1##. Linear Programming in some sense was designed to deal with things like this. 'Regular' matrix solvers are not. I would[I] not recommend[/I], in effect, creating Simplex from scratch via coming up with solutions via 'regular' solvers and doing lots of pivotting on your own... it is much better to use an off the shelf, highly efficient LP solver. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Linear and Abstract Algebra
Forcing conditions in a solution of an under-determined system
Back
Top