You can also try to use the pseudo-inverse $A^{+}$ in LaTeX. It is also
called the Moore-Penrose inverse.
In this case (with variable names in thread and `AP` used for the inverse)
it is:
AP = A'*inv(A*A')
And then we have ('x' is the solution to the equations):
x = AP*v
and as it should be
A*x == v
is true.
Hope this helps.
-- Dan
On Friday, July 15, 2016 at 2:50:01 PM UTC-4, Kurolong wrote:
>
> Hey Guys and Gals ^^
> I'm having trouble with Julia. Maybe one of you can help me out
> The program i am writing requires the
> linear-equation-system-solver(command "\") in the folder
> "Julia-0.4.5\share\julia\base\linalg".
> Now my problem is that i need the equation solved strictly on integers, an
> approximate solution is of no use to me, which is why i tried working with
> the "Rational" Type.
> Curiously, the solver seems to work for the Rational Type if and only if
> no pivoting is required. Otherwise, the following Error is thrown:
>
> WARNING: pivoting only implemented for Float32, Float64, Complex64 and
> Complex128
> ERROR: LoadError: OverflowError()
> in * at rational.jl:188
> [inlined code] from linalg/generic.jl:471
> in reflector! at no file:0
> in A_ldiv_B! at linalg/qr.jl:346
> in \ at linalg/qr.jl:398
> in \ at linalg/dense.jl:450
> in include at boot.jl:261
> in include_from_node1 at loading.jl:320
> while loading C:\users\<username
> omitted>\documents\julia-0.4.5\sg_project\v0.3\Test02.jl, in expression
> starting on line 3
>
> Code to reproduce the Error:
>
> A=[[2//1,0//1] [3//1,3//2] [1//1,3//2]]
> v=[2//1,0//1]
> A\v
>
> Now i am under the impression that i could build a relatively simple
> workaround if i knew exactly where in the developer's code the actual
> problem is, but i am confused by the whole organization of the thing.
> Building my own solver could certainly be done, but this will most likely
> be ineffecient. Unfortunately, runtime is very important here, as the
> method i am currently devising is supposed to be embedded in some very
> expensive loops.
>
> I am a very unexperienced programmer and will likely not understand much
> programmertalk, but i am a mathematician and will probably have little
> problems in this respect.
>
> Maybe you have some ideas how to handle this problem.
>
> Thank you in advance for taking the time to look at my problem :)
>
