title: Solve Underdetermined System of Equations for Sparse Solution
body: <ul>
  <li>A, C are m x n rectangular matrix. </li>
  <li>B is a n x n square matrix. </li>
  <li>B is not symmetric.</li>
  <li>B, C are known</li>
  <li>AB = C. </li>
  <li>B is singular.</li>
  </ul>
  
  <p>I could use the moore-penrose inverse of B to get A = CB<sup>+</sup>.</p>
  
  <p>But that seems to make A have many non-zero elements.</p>
  
  <p>If I want an A (among all possible solutions) that is quite sparse, what solvers can I try?</p>
  
  <p>Should I use BDCSVD, as in <a href="https://eigen.tuxfamily.org/dox/group__LeastSquares.html" rel="nofollow noreferrer">here</a>?</p>
  
  <p>Thanks.</p>