Man-Chung Yeung
Department of Mathematics
Dept. 3036
1000 East University Avenue
Laramie, WY 82071

307-766-4012 (office)
myeung@uwyo.edu

Education
Ph.D., UCLA, 1997

Publications
Teaching
Professional Activities


Dr. Yeung is an associate professor in the Department of Mathematics at University of Wyoming. He obtained his PhD from UCLA in Sept., 1997 under the supervision of Prof. T. Chan. After he graduated from UCLA, he spent one year in the Department of Computer Science at University of Minnesota as a postdoc under the direction of Profs Boley and Saad. Then he returned to UCLA to work on a project supported by Chevron. He had taught at UC Irvine from 1999 to 2001. Dr. Yeung's research fields of interest are in iterative methods, preconditioning techniques, multigrid and domain decomposition, and parallel computations. He has published over ten academic papers in the top journals in the field of scientific computing. The research works he has done so far can be divided into two parts:

Dr. Yeung studied and analysed circulant preconditioners for Toeplitz systems. For Toeplitz matrices T generated by positive 2 pi-periodic continuous functions, he, together with Prof. R. Chan at Chinese University of Hong Kong, showed that the circulantly preconditioned system can be solved with CG method within a finite number of steps and this number is independent of the system size. If the generating functions are not continuous, however, the number of iterations required for CG to converge increases at least like O(log n), where n is the system size. Moreover, they found out that good circulant preconditioners can be constructed from kernels. Most of the works have been summarized in a survey paper by R. Chan and Ng which was published in SIAM Review.

Dr. Yeung studied Krylov subspace metods for the solutions of linear systems. He, together with Prof. T. Chan, derived an effective algerithm named ML(k)BiCGSTAB which combines the advantages in both BiCGSTAB and GMRES and which can also be viewed as a bridge connecting them. Compared with BiCGSTAB and GMRES(k), ML(k)BiCGSTAB seems to have more stable performance. Moreover, when he was a postdoc at University of Minnesota, Dr. Yeung with Prof. Saad, et al. generated CG method to a deflated CG method for the soltions of systems with multiple right-hand sides.

Dr. Yeung's current research is focused on parallel computations and multigrid method. He is planning to develop iterative methods which can be implemented efficiently in parallel environments.

Publications:

   M. Yeung, "ML(n)BiCGSTAB: reformulation, analysis and implementation",
   Report 09-01, Math. Dept., UW (a draft subject to change).  paper.pdf,  Matlab codes

   M. Yeung and D. Boley, " Transpose-free multiple Lanczos and its application in Pade approximation ",
   Journal of Computational and Applied Mathematics, Vol 177/1 pp. 101-127, 2005.  paper.pdf

   Gui-Bing Zhao, Xudong Hu, Man-Chung Yeung, Ovid A. Plumb, and Maciej Radosz, " Nonthermal-Plasma Reactions
   of Dilute Nitrogen Oxide Mixtures: NOx-in-Nitrogen ",   Ind. Eng. Chem. Res., 2004, 43, 2315-2323.  paper.pdf

   M. Yeung, " Probabilistic Analysis of Complex Gaussian Elimination without Pivoting ",
   Linear Algebra Appls., 384 (2004), 109-134.  paper.pdf

   Y. Saad, M. Yeung, J. Erhel and F. Guyomarc'h, " A deflated version of the Conjugate Gradient Algorithm ",
   SIAM J. Sci. Comput. Vol. 21, No. 5, pp. 1909-1926, 2000.  paper.pdf

   M. Yeung and T. Chan, " ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors ",
   SIAM J. Sci. Comput. Vol. 21, No. 4, pp.1263-1290, 1999.  paper.pdf   Matlab code

   T. Chan, E. Chow, Y. Saad and M. Yeung, " Preserving Symmetry in Preconditioned Krylov Subspace Methods ",
   SIAM J. Sci. Comput. Vol. 20, No. 2, pp.568-581, 1998.  paper.pdf

   M. Yeung and T. Chan, " Probabilistic Analysis of Gaussian Elimination without Pivoting ",
   SIAM J., Matrix Anal. Appl., pp. 499-517, April 1997.  paper.pdf

   R. Chan and M. Yeung, " A Note on the Besov Space B(2, 1/2) ",
   SEA Bull. Math., 19 (1995), 75-81.  paper.pdf

   S. Chung and M. Yeung, " On a Subspace Related to the Korovkin Closure ",
   SEA Bull. Math., 18 (1994), 11-18.  paper.pdf

   M. Yeung and R. Chan, " Circulant Preconditioners for Toeplitz Matrices with Piecewise Continuous Generating Functions ",
   Math. Comp., 61 (1993), 701-718.  paper.pdf

   R. Chan and M. Yeung, " Circulant Preconditioners for Complex Toeplitz Matrices ",
   SIAM J. Numer. Anal., 30 (1993), 1193-1207.  paper.pdf

   R. Chan and M. Yeung, " Jackson's Theorem and Circulant Preconditioned Toeplitz Systems ",
   J. Approx. Theory, 70 (1992), 191-205.  paper.pdf

   R. Chan and M. Yeung, " Circulant Preconditioners Constructed from Kernels ",
   SIAM J. Numer. Anal, 29 (1992), 1093-1103.  paper.pdf

   R. Chan and M. Yeung, " Circulant Preconditioners for Toeplitz Matrices with Positive Continuous Generating Functions ",
   Math. Comp., 58 (1992), 233-240.  paper.pdf

   R. Chan, X. Jin and M. Yeung, " The Spectra of Super-optimal Circulant Preconditioned Toeplitz Systems ",
   SIAM J. Numer. Anal., 28 (1991), 871-879.  paper.pdf

   R. Chan, X. Jin and M. Yeung, " The Circulant Operator in the Banach Algebra of Matrices ",
   Linear Algebra Appls., 149 (1991), 41-53.  paper.pdf

Teaching, Spring 2008:

      Calculus I, 2200

      Numerical Analysis, 4340

Professional Activities

  Grants:
     Recipient of a NSF grant as PI, 2003-2006.
         

  Services:

      3. Yeung participated in the Summer Research Apprentice Program 2004 and supervised (with Jon Held) Shawn Sickel from

          Saint Thomas Aquinas High School, FL. This program is funded by Wyoming NSF EPSCoR. Here is the poster,

          presentation and paper that Shawn made in this program.

      2. Yeung is participating in the graduate committee of Math Dept..

      1. Yeung was on Satoko Kurita’s Doctoral Committee in 2002.

  Conferences:

     8.   Gene Golub Memorial Conference, Feb. 29 – Mar. 1, 2008,  University of Massachusetts, Dartmouth. (Talk: Analysis of ML(n)BiCGSTAB)

     7.   14th Conference of the International Linear Algebra Society, July 16-20, 2007, Department of Mathematics,

           Shanghai University, Shanghai, China. (Talk: Anal. of mlbicgstab)

     6.   Householder Symposium XVI, May 23-27, 2005, Seven Springs Mountain Resort, Champion, Pennsylvania. (Talk: Pade approx.)    

     5.   11th Conference of the International Linear Algebra Society, July 19 - 22, 2004, University of Coimbra, Portugal. (Talk: Complex GE)

     4.   Eighth Copper Mountain conference on iterative methods, March 28 - April 2, 2004.

     3.   SIAM Conference on Applied Linear Algebra, July 15 - 19, 2003, The College of William & Mary Williamsburg, VA. (Talk: ML(k)BiCGSTAB )

     2.   Sixth IMACS International Symposium on Iterative Methods in Scientific Computing, March 27-30, 2003. (Talk: ML(k)BiCGSTAB )

     1.   IMA workshop: Optimization in Simulation Based Models, January 9-16, 2003.