title: Measure computational complexity of solving a linear system Ax=b by increasing size of A
body: <p>I have a linear equation</p>
  
  <pre><code>Ax=b
  </code></pre>
  
  <p>where <code>A</code> is non-singular matrix <code>N×N</code>, and <code>x,b</code> are vector <code>N×1</code>; <code>A,b</code> are given and I want to find x</p>
  
  <p>It is clear that x can be found by x=A^(−1)*b. I would like to measure  the computational complexity when <code>N</code> increasing.</p>
  
  <p>In MATLAB, I used the code x=A\b. I know that MATLAB will choose a best algorithm to find the solution. In analysis, I know that the computational complexity grows as N^3 when N is increases. How can I fit/measure computational complexity between simulation and analysis of above equation when N increasing? </p>