0
votes
0answers
11 views

Canonical forms and basic solutions of linear equations

My notes tell me that this system in the form Ax=b , A has 4 bases, I believe it is something to do with pivot columns? Which 4 are bases? From the bases, how do I find the canonical form and thus ...
0
votes
1answer
30 views

Linear programming and the simplex method

I am trying to solve this system of equations. My approach would be to introduce slack variables and then somehow use the simplex algorithm to solve this. Can anyone show me how this is done?
2
votes
4answers
93 views

Solution to a system of nonlinear equations

Do you know any method to solve the following system of nonlinear equations ? $\begin{equation} 141,3829=A+\frac{B}{323}+5,78C+F323^{E}\\ 69,07645=A+\frac{B}{333}+5,81C+F333^{E}\\ ...
0
votes
0answers
41 views

Strategies to work with system of trigonometric inequality

I'm trying solve this problem using matlab, anybody know good strategies to work with system of trigonometric inequalities such as $ ...
2
votes
1answer
64 views

Mathematically choose the better discount

This may seem like a homework problem because it is. However it is not my homework - it belongs to the child I am tutoring, so please feel free to give a full answer, as I will only lead the child ...
1
vote
1answer
48 views

solving a linearly-constrained sparse linear least-squares problem

Given the system of equations $Ax=b$, subject to $Cx\le d$ where $A$ is an $n\times m$ matrix (with $n>m$) and is very large and sparse. As an example $A$ can have $3126250\times 2740$ elements. ...
0
votes
1answer
42 views

How can I find four colors with maximum equal difference?

I need to find four colors, expressed as triple $(r_i, g_i, b_i)$ where $0 \le r_i,g_i,b_i \le 1$, $0 \le i \le 3$. Define color difference as $D_{i,j}=\sqrt{(r_i-r_j)^2+(g_i-g_j)^2+(r_i-r_j)^2}$. ...
0
votes
0answers
76 views

Solve the system of inequalities. Optimization problem.

I have a set of linear inequalities as follow: ...
1
vote
0answers
91 views

Algebraic manipulation of Lyapunov function

I have a problem I would like some feedback on. I have spent 6 hours on it examining various techniques (numerically and analytically). I need to find the values of $k$ for which $x^2+ky^2$ is a ...
0
votes
1answer
27 views

Graph Laplacian - Spectral Clustering with Regularization

Assume a graph $G=(V,E)$ where the vertices $V$ are points in ${{R}^{D}}$ with $\left| V \right|=n$. The edges $E$ are represented by a $n\times n$ affinity matrix $W$. Consider the graph Laplacian ...
1
vote
3answers
2k views

How to plot a phase portrait for this system of differential equations?

I beg your help.. I'd like the phase portrait for this system. I don't know how to use Mathematica/Matlab ... :( If anyone can make this portrait and post a print screen here, I would thank you ...
1
vote
1answer
86 views

A System of differential Equations

How can I analyze the phase diagram for this system of differential eqs? This field is not my area of my expertise, so please be generous with the answers. I appreciate quick references as well. ...
1
vote
1answer
40 views

The most optimal way to solve this set of non-linear equations in high dimensions

So I have a series of non-linear equations which I wish to solve as fast as possible, to illustrate for the case of $n = 4$, I have the following equations: \begin{gather*} ...
4
votes
0answers
34 views

Is there a name for systems of equations with min and max functions included?

In a big project I'm working on, I'm running into systems of equations that look like the following: $$a = \min(b, c)$$ $$b = d^2 + a$$ $$c = \max(a + b, d)$$ Basically, nonlinear systems of ...