News

• Our algorithms for (singular) totally nonnegative matrices compute exactly the zero eigenvalues and their corresponding Jordan blocks in what we believe is the first example of Jordan blocks being computed stably in floating point arithmetic. This solves completely the eigenvalue problem for the class of irreducible totally nonnegative matrices. See our paper and software.
• We transcribed Ian G. Macdonald's unpublished manuscripts:
  • Hypergeometric Functions I
  • Hypergeometric Functions II, q-analogues
  and developed a new course at the Department of Mathematics.

Teaching

• Fall 2018: Math 285. The rest of the courses are on CANVAS.
• Spring 2018: Math 32 and Math 243M
• Fall 2017: Math 32 and Math 143M
• Spring 2017: Math 32 and Math 243M
• Fall 2016: Math 30 and Math 143M
• Spring 2016: Math 129A and Math 243M
• Fall 2015: Math 129A and Math 143M
• Fall 2014: Math 30 and Math 243A
• Math 30 and Math 143C, Spring 2014
• Math 243B, Fall 2013
• Math 32 and Math 243A, Fall 2012
• Math 143M and CAMCOS Project, Fall 2011
• Math 70 and Math 143M, Fall 2010
• Math 70, Fall 2009
• Math 30, Spring 2009

Research

Items of interest:

• Developed theory and algorithms for accurate computations with sign regular, totally nonnegative, polynomial Vandermonde, generalized Vandermonde, semiseparable, and M-matrices
• Developed the first algorithm for computing the eigenvalues of a nonsymmetric matrix to high relative accuracy in O(n³) time
• Developed the first stable algorithm to stably compute a Jordan block (for irreducible totally nonnegative matrices)
• Developed the fastest algorithm for computing the hypergeometric function of a matrix argument

Awards

• Householder Award (for ``Best Dissertation in Numerical Linear Algebra in the period 2002-2004''), honorable mention
• Outstanding Graduate Student Instructor, University of California, Berkeley, 1999
• Second Prize, International Mathematics Olympiad, Beijing, China, 1990