Yuanzhe Xi


Postdoctoral research associate
University of Minnesota
Department of Computer Science and Engineering
5-250 Keller Hall
200 Union St. S.E.
Minneapolis, MN, 55455
Office: 1-612-625-0519
Email: yxi@umn.edu
Curriculum Vitae

 


Appointment

 Postdoctoral Research Associate August 2014-present
  - Mentor: Prof. Yousef Saad

 

Education

 Purdue University West Lafayette, USA
  Ph.D. Applied Mathematics 2009 - 2014
  - Advisor: Prof. Jianlin Xia
 Purdue University West Lafayette, USA
  M.S. Computational Finance2012 - 2014
 Dalian University of TechnologyDalian, China
  B.S Computational Mathematics2005 - 2009

 

Research Interests
Fast direct solvers
Preconditioning techniques
Fast eigenvalue solvers
Fast Toeplitz/Hankle solvers
Numerical analysis
High performance computing
Machine learning
Perturbation theory

 

Publications
Y. Xi and Y. Saad, A rational function preconditioner for indefinite sparse linear systems, accepted, SIAM J. Sci. Comput., 2017.
Y. Xi and Y. Saad, Computing partial spectra with least-squares rational filters, SIAM J. Sci. Comput., 38 (2016), pp. A3020-A3045.(Journal article link)
Y. Xi and J. Xia, On the stability of some hierarchical rank structured matrix alogrithms, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1279-1303. (Journal article link)
R. Li, Y. Xi, E. Vecharynski, C. Yang and Y. Saad, A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems, SIAM J. Sci. Comput., 38 (2016), pp. A2512-A2534. (Journal article link)
R. Li, Y. Xi, and Y. Saad, Schur complement based domain decomposition preconditioners with low-rank corrections, Numer. Linear Algebra Appl., 23(4) (2016), pp. 706-729. (Journal article link)
Y. Xi, R. Li, and Y. Saad, An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 235-259. (Journal article link)
J. Xia, Y. Xi, S. Cauley, and V. Balakrishnan, Fast sparse selected inversion, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 1283-1314. (Journal article link)
S. Cauley, Y. Xi, B. Bilgic, J. Xia, E. Adalsteinsson, V. Balakrishnan, L. Wald, and K. Setsompop, Fast reconstruction for multi-channel compressed sensing using a hierarchically semiseparable solver, Magn. Reson. Med., 73 (2015), pp. 1034-1040. (Journal article link)
Y. Xi, J. Xia, and R. Chan, A fast randomized eigensolver with structured LDL factorization update, SIAM J. Matrix Anal. Appl., 35 (2014), pp. 974-996. (Journal article link)
Y. Xi, J. Xia, S. Cauley, and V. Balakrishnan, Superfast and stable structured solvers for Toeplitz least squares via randomized sampling, SIAM J. Matrix Anal. Appl., 35 (2014), pp. 44-72. (Journal article link)
J. Xia, Y. Xi, and M. Gu, A superfast structured solver for Toeplitz linear systems via randomized sampling, SIAM J. Matrix Anal. Appl., 33 (2012), pp. 837-858. (Journal article link)
SMASH: Structured matrix approximation by separation and hierarchy, with D. Cai, E. Chow and Y. Saad, submitted to SIAM J. Matrix Anal. Appl., 2017.
Efficient solution methods for Gaussian and related kernel systems, with D. Cai, E. Chow and Y. Saad, preprint, 2016.
Superfast sparse arbitrary inversion, with X. Liu, J. Xia and M. de Hoop, preprint, 2016.
Newton iterations for the solution of symmetric generalized eigenvalue problems, with V. Kalantzis and Y. Saad, preprint, 2017.
Rational filtering algebraic substructuring techniques for the solution of large-scale generalized symmetric eigenvalue problems, with V. Kalantzis and Y. Saad, preprint, 2017.

 

Software
EigenValues Slicing Library (EVSL)

Superfast and stable Toeplitz linear system and least-squares direct solvers

 

Presentations
Exploiting data-sparse structures in numerical linear algebra
   - Colloquium, Michigan State University, East Lansing, MI, USA (Feb 2017).
Exploiting data-sparse structures in scientific computing
   - Colloquium, The Ohio State University, Columbus, OH, USA (Nov 2016).
Fast contour-integral preconditioner
   - Workshop on Fast Direct Solvers, Purdue University, West Lafayette, IN, USA (Nov 2016).
Exploiting data-sparse structures in scientific computing
   - CCAM lunch seminar, Purdue University, West Lafayette, IN, USA (Nov 2016).
Polynomial and rational filtering for eigenvalue problems
   - CCAM special lecture, Rice University, Houston, TX, USA (Sep 2016).
A rational function preconditioner for indefinite sparse matrices
   - SIAM Annual Meeting, 2016, Boston, USA (July 2016).
Spectrum slicing by polynomial and rational function filtering
   - SIAM Annual Meeting, 2016, Boston, USA (July 2016).
A rational function preconditioner for highly indefinite sparse matrices
   - GMIG annual meeting, Rice University, Houston, TX, USA (April 2016).
Spectrum slicing by polynomial and rational function filtering
   - Midwest Numerical Analysis Day, La Crosse, WI, USA (April 2016).
An algebraic multilevle preconditioner with low-rank corrections for sparse symmetric matrices
   - SIAM Conference on Applied Linear Algebra, Atlanta, GA, USA (Oct. 2015).
An arbitrary inversion algorithm for large sparse matrices
   - SIAM Annual Meeting 2013, San Diego, CA, USA (July 2013).
Superfast algorithms for Toeplitz matrices via randomized sampling
   - New Frontiers in Numerical Analysis and Scientific Computing - Kent State University, Kent, USA (April 2013).
Superfast structured inversion for extracting diagonal entries
   - Geo-Mathematical Imaging Group Project Review and Advisory Board Meeting - Chicago, USA (April 2013).
A fast eigensolver for discretized PDEs from irregular mesh
   - Geo-Mathematical Imaging Group Project Review and Advisory Board Meeting - Purdue University, West Lafayette, USA (April 2012).
Superfast algorithms for Toeplitz problems
   - 4th SIAM Annual Computational Science and Engineering Student Conference (CSESC) - Purdue University, West Lafayette, USA (April 2012).
Introduction to matrix computation
   - Student colloquium - Purdue University, West Lafayette, USA (Dec 2011).
A superfast and stable solver for Toeplitz linear systems via randomized sampling
   - Midwest Numerical Analysis Day - Purdue University, West Lafayette, USA (May 2011).
A superfast structured solver for Toeplitz linear Systems via randomized sampling
   - 3rd SIAM Annual Computational Science and Engineering Student Conference (CSESC) - Purdue University, West Lafayette, USA (April 2011).

 

Honors
AMS-Simons Travel Grant, 2016-2018
SIAM 2017 Annual Meeting Logo selected from Figure 3.1(c) of our paper 'An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices'
SIAG/LA sponsored minisymposium 'Innovative Methods for Large Scale Eigenvalue Solutions' at SIAM Annual meeting, Boston, MA, USA, 2016
SIAG/LA sponsored minisymposium 'Recent Developments in Low-rank Preconditioning Techniques' at SIAM conference on Applied Linear Algebra, Altanta, GA, USA, 2016
Purdue Research Foundation Fellowship, 2013-2014
Third place for paper competition at CSESC-Purdue University, April 2012
Travel Awards from the following conferences:
   - SIAM conference on Applied Linear Algebra 2015, Atlanta, GA, USA, 2015
   - ICERM workshop on Numerical methods for Large-Scale Nonlinear Problems and Their Applications, Providence, RI, USA, 2015
   - 13th workshop on the DOE Advanced CompuTational Software (ACTS) Collection, Berkeley, CA, USA, 2012
   - International Conference on the Frontier of Computational and Applied Mathematics: Tony Chan's 60th Birthday Conference, UCLA, Los Angeles, CA, USA, 2012
   - Challenges in Geometry, Analysis, and Computation: High-Dimensional Synthesis Conference at Yale University, New Haven, Ma, USA, 2012
Honorable Mention Award in MCM (Mathematical Competition in Modeling), 2008

 

Professional Experience

 Research Assistant(Purdue University)
  - Working on fast algorithms for structured and sparse matrices Spring 2012- Spring 2014
 Numerical Analysis (MA514)(Purdue University)
  - Teaching Assistant Fall 2011
 Plane Analytic Geometry And Calculus I (MA154)(Purdue University)
  - Course Instructor Spring 2011
 Multivariate Calculus (MA161)(Purdue University)
  - Recitation lecturer Fall 2010
 Multivariate Calculus (MA261)(Purdue University)
  - Recitation lecturer Spring 2010
 Multivariate Calculus (MA261)(Purdue University)
  - Recitation lecturer Fall 2009

 

Journal Referee Activity
Parallel Computing
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Numerical Algorithms
Numerical Linear Algebra with Applications
Journal of Computational Statistics & Data Analysis

 

Conference Attended
Frontiers in PDE-constrained Optimization, IMA, June 06-10, 2016
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications, ICERM, August 31-September 4, 2015
Fast Direct Solvers for Elliptic PDEs, Dartmouth College, June 23-29, 2014
13th Workshop on the DOE Advanced Computational Software (ACTS) Collection, Berkeley, August 14-17, 2012.
The International Conference on the Frontier of Computational and Applied Mathematics: Tony Chan's 60th Birthday Conference, UCLA, June 8-10, 2012.
Challenges in Geometry, Analysis, and Computation: High-Dimensional Synthesis Conference at Yale University, June 4-6, 2012.

 

 

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last modified: 10/12/2016