title: Solving linear equations during inverse iteration
body: <p>I am using OpenCL to calculate the eigenvectors of a matrix. AMD has an <a href="http://developer.amd.com/sdks/AMDAPPSDK/samples/Pages/default.aspx" rel="nofollow noreferrer">example</a> of eigenvalue calculation so I decided to use inverse iteration to get the eigenvectors.</p>
  
  <p>I was following the algorithm described <a href="http://web.eecs.utk.edu/~dongarra/etemplates/node96.html" rel="nofollow noreferrer">here</a> and I noticed that in order to solve step 4 I need to solve a system of linear equations (or calculate the inverse of a matrix).</p>
  
  <p><img src="https://i.stack.imgur.com/bfqOW.png" alt="Inverse Iteration"></p>
  
  <p>What is the best way to do this on a GPU using OpenCL? Are there any examples/references that I should look into?</p>
  
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  <p>EDIT: I'm sorry, I should have mentioned that my matrix is symmetric tridiagonal. From what I have been reading this could be important and maybe simplifies the whole process a lot</p>