Appointment
Education
Purdue University  West Lafayette, USA 
Ph.D. Applied Mathematics  2009  2014 
 Advisor: Prof. Jianlin Xia  
Purdue University  West Lafayette, USA 
M.S. Computational Finance  2012  2014 
Dalian University of Technology  Dalian, China 
B.S Computational Mathematics  2005  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 leastsquares rational filters, SIAM J. Sci. Comput., 38 (2016), pp. A3020A3045.(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. 12791303. (Journal article link)
R. Li, Y. Xi, E. Vecharynski, C. Yang and Y. Saad, A ThickRestart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems, SIAM J. Sci. Comput., 38 (2016), pp. A2512A2534. (Journal article link)
R. Li, Y. Xi, and Y. Saad, Schur complement based domain decomposition preconditioners with lowrank corrections, Numer. Linear Algebra Appl., 23(4) (2016), pp. 706729. (Journal article link)
Y. Xi, R. Li, and Y. Saad, An algebraic multilevel preconditioner with lowrank corrections for sparse symmetric matrices, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 235259. (Journal article link)
J. Xia, Y. Xi, S. Cauley, and V. Balakrishnan, Fast sparse selected inversion, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 12831314. (Journal article link)
S. Cauley, Y. Xi, B. Bilgic, J. Xia, E. Adalsteinsson, V. Balakrishnan, L. Wald, and K. Setsompop, Fast reconstruction for multichannel compressed sensing using a hierarchically semiseparable solver, Magn. Reson. Med., 73 (2015), pp. 10341040. (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. 974996.
(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. 4472.
(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. 837858.
(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 largescale generalized symmetric eigenvalue problems, with V. Kalantzis and Y. Saad, preprint, 2017.
Software
EigenValues Slicing Library (EVSL)
Superfast and stable Toeplitz linear system and leastsquares direct solvers
Presentations
Exploiting datasparse structures in numerical linear algebra
 Colloquium, Michigan State University, East Lansing, MI, USA (Feb 2017).
Exploiting datasparse structures in scientific computing
 Colloquium, The Ohio State University, Columbus, OH, USA (Nov 2016).
Fast contourintegral preconditioner
 Workshop on Fast Direct Solvers, Purdue University, West Lafayette, IN, USA (Nov 2016).
Exploiting datasparse 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 lowrank 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
 GeoMathematical Imaging Group Project Review and Advisory Board Meeting  Chicago, USA (April 2013).
A fast eigensolver for discretized PDEs from irregular mesh
 GeoMathematical 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
AMSSimons Travel Grant, 20162018
SIAM 2017 Annual Meeting Logo selected from Figure 3.1(c) of our paper 'An algebraic multilevel preconditioner with lowrank 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 Lowrank Preconditioning Techniques' at SIAM conference on Applied Linear Algebra, Altanta, GA, USA, 2016
Purdue Research Foundation Fellowship, 20132014
Third place for paper competition at CSESCPurdue 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 LargeScale 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: HighDimensional 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 PDEconstrained Optimization, IMA, June 0610, 2016
Numerical Methods for LargeScale Nonlinear Problems and Their Applications, ICERM, August 31September 4, 2015
Fast Direct Solvers for Elliptic PDEs, Dartmouth College, June 2329, 2014
13th Workshop on the DOE Advanced Computational Software (ACTS) Collection, Berkeley, August 1417, 2012.
The International Conference on the Frontier of Computational and Applied Mathematics: Tony Chan's 60th Birthday Conference, UCLA, June 810, 2012.
Challenges in Geometry, Analysis, and Computation: HighDimensional Synthesis Conference at Yale University, June 46, 2012.
