Advanced numerical method is a course to introduce and to survey the
<br>recent development of numerical algorithms.  The topics may include
<br>
<br>1. Review of linear algebra.
<br>2. Sparse matrix techniques. (representation, multiplication, direct solvers)
<br>3. Recursive algorithms. (FFT, Fast Multipole method, Multigrid)
<br>4. Communication complexity.
<br>5. Mixed precision algorithms.
<br>6. Matrix functions.
<br>7. Numerical methods for tensor and high dimensional data.
<br>
<br>For each topic, we will focus on its algorithms and numerical properties, 
<br>accuracy, performance, and data storage.  Students who take this course 
<br>need to attend the lecture, present papers, and implement some of the 
<br>algorithms. Implementation may use Matlab, C, or Fortran.
<br>
<br>Pre-request: linear algebra, programming