I have a symbolic matrix that depends on a complex parameter q. Let the matrix be A(q) and b a column vector. I would like to simultaneously solve the equations
A*b==0; b'*b==1;
using the solve command (preferably the numerical variant vpasolve). The variables to be found are both b and q. I am not quite sure about the syntax on how to do this and would appreciate any help on it. My main problem is that the equation is partially given in matrix form and the searched variable is a vector.
Do I have to resort to fsolve to achieve this? Or is there a way without defining a function?
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I'm currently working on solving an equation that involves a symmetric matrix C with 4 unknown variables, and a vector A of the same dimension. The equation I'm trying to solve is:
[C]*{A}=0 (1)
where * denotes matrix multiplication and { } denotes a vector.
The dimension of the C matrix can be as large as 100x100 or more, and I'm trying to define the unknown variables in C in a way that solves equation (1). One approach I've tried is to calculate the determinant of C, |[C]|=0, and solve for the 4 different variables inside.
However, when the dimension of the matrix is large, my current method in Mathematica is not able to solve the problem. I'm wondering if anyone has any suggestions for me to solve this equation more efficiently.
I'm open to using other programming languages such as Matlab or Python as well. Any suggestions or advice would be greatly appreciated.
Thank you in advance for your help and guidance.
I have tried solving this problem with 25*25 dimension. However, this size is not enough for the percision that I want for the variables.
I am trying to use matlab's fsolve to solve a system of 4 nonlinear equations. I'm solving the system for each point in a grid of parameters by looping through each point and calling the fsolve function.
My problem is that I need to give some of these parameters as input to fsolve. These inputs should be treated as constants for each separate solving of the system.
Can anyone help me?
you can just do:
result = fsolve(#(x) eqns(a,b,c,d),guess)
and in addition make the function eqns() with your equation set.
I have a matrix equation and I want to solve it in MATLAB. The equation is
X^(-1)AX=B.
Where X is an unknown symmetric 3x3 matrix, A is known and B is a diagonal matrix (There isn't any condition on B's elements, just diagonal).
Please help me solve this problem!
From the information you've given it appears that you are looking for a symbolic solution which Matlab is not the best at (usually Mathematica is prefered or check out Wolfram Alpha). If you absolutely need Matlab then you could use the 'solve()' command.
However, honestly you are dealing with a rather simple linear system of small dimensions so it is probably easiest to just work this out by hand. Check out Matrix Cookbook for help. Also it really just looks like you are just trying to solve for the eigenvector matrix so possibly the command eig() might help ??
I have a set of 4 PDEs:
du/dt + A(u) * du/dx = Q(u)
where,u is a matrix and contains:
u=[u1;u2;u3;u4]
and A is a 4*4 matrix. Q is 4*1. A and Q are function of u=[u1;u2;u3;u4].
But my questions are:
How can I solve above equation in MATLAB?
If I solved it by PDE functions of Matlab,can I convert it to a
simple function that is not used from ready functions of Matlab?
Is there any way that I calculate A and Q explicitly. I mean that in
every time step, I calculate A and Q from data of previous time step
and put new value in the equation that causes faster run of program?
PDEs require finite differences, finite elements, boundary elements, etc. You can also turn them into ODEs using transforms like Laplace, Fourier, etc. Solve those using ODE functions and then transform back. Neither one is trivial.
Your equation is a non-linear transient diffusion equation. It's a parabolic PDE.
The equation you posted has the additional difficulty of being non-linear, because both the A matrix and Q vector are functions of the independent variable q. You'll have to start by linearizing your equations. Solve for increments in u rather than u itself.
Once you've done that, discretize the du/dx term using finite differences, finite elements, or boundary elements. You should start with a weighted residual integral formulation.
You're almost done: Next to integrate w.r.t. time using the method of your choice.
It's not trivial.
Google found this: maybe it will help you.
http://www.mathworks.com/matlabcentral/fileexchange/3710-nonlinear-diffusion-toolbox
I have to analyze 802.11 saturation throughput using matlab, and here is my problem. I'm trying to solve parametric equations below (parameters are m,W,a) using solve function and i get
Warning: Explicit solution could not be found
How could I solve above equations using matlab?
I guess you were trying to find an analytical solution for tau and p using symbolic math. Unless you're really lucky with your parameters (e.g. m=1), there won't be an analytical solution.
If you're interested in numerical values for tau and p, I suggest you manually substitue p in the first equation, and then solve an equation of the form tau-bigFraction=0 using, e.g. fzero.
Here's how you'd use fzero to solve a simple equation kx=exp(-x), with k being a parameter.
k = 5; %# set a value for k
x = fzero(#(x)k*x-exp(-x),0); %# initial guess: x=0