All Questions
8
questions
3
votes
1
answer
201
views
How to find a unimodular integer matrix $T$ satisfying $T^\top A T=B$ given symmetric integer matrices $A,B$?
Given two unimodular symmetric integer matrices $A$ and $B$,
I asked how to find a unimodular integer $T$ that satisfies this nonlinear relation between $T$ and $A,B$ like this in Mathematica:
...
- 251
8
votes
2
answers
388
views
Given square matrices A and B, how to solve T obeys Transpose[T]. A . T = B?
Dear Mathematica experts,
Given two square matrices, A and B, how do we use Mathematica to solve a matrix T such that T satisfies this matrix equation? (Here we have A,B,T $\in$ general linear matrix ...
- 251
1
vote
0
answers
97
views
Optimizing my code to solve nonlinear system
I have solved a non-linear system using Eliminate[] and Solve[], using a really nice answer found here I am able to use ...
-1
votes
1
answer
106
views
Solving Nonlinear System
I am solving a $3X3$ non-linear system (posted also in mathematics).After some simplifying assumptions it looks like this:
$$K c_1 x_1=(1-x_2)(1-x_3)+a_1(1-x_2)x_3+a_2(1-x_3)x_2+a_3x_3x_2$$
$$K c_2 ...
3
votes
2
answers
209
views
Fitting an exponential system
Consider the following system over a periodic array, where $1\leq j\leq n$,
$$
y_j= \sum_{k=0}^m \frac{e^{-\sum_{|i|\leq k}(k-|i|)x_{j+i}}-e^{-\sum_{|i|\leq k}(k+1-|i|)x_{j+i}}}{\sum_{|i|\leq k} x_{j+...
- 4,903
1
vote
1
answer
92
views
Minimize Reprojection Error [closed]
I have a function
Point= {2, 0, 0, 1};
x = ProjectionMatrix[f] . (RotateMatrix . Point + t)
Return[x];
x is a 3D Vector.
where the Projection Matrix is
...
10
votes
2
answers
1k
views
Problem with optimal control and Pontryagin's maximum principle
For dynamic system:
$\dot{x}=\frac{df}{dx}+u$
where $f=e^{-x^2}$
It is necessary to develop optimal control, minimizing criterion:
$J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $
Algorithm:
We ...
- 2,444
3
votes
1
answer
497
views
Runge-Kutta to find maximum of system of ODEs
I'm trying to understand a code for finding the minimum and maximum for a system of ODEs. Here is the code:
...
- 133