Lihong Zhi, Professor
Mathematics Mechanization Research Center
Institute of Systems Science
Academy of Mathematics and System Sciences
Academia Sinica, Beijing, China
Tel: 86-10-82541838, FAX: 86-10-82541809
lzhi at mmrc.iss.ac.cn



 
Lihong Zhi

 
Education

    Ph.D. Computer Algebra(July 1996)
    Institute of Systems Science, Academia Sinica, Beijing 100190, China
    B.Sc. Mathematics(July 1991)
    Peking University, Beijing 100871, China

Related Work Experience

    Professor (March 2009 - Present)
    Academy of Mathematics and Systems Science, CAS, Beijing
    Associate Professor (April 2003 - February 2009)
    Academy of Mathematics and Systems Science, CAS, Beijing
    Assistant Professor (July 1996 - 2003)
    Institute of Systems Science, CAS, Beijing

Editorial Responsibilities

·         SIAM Journal on Applied Algebra and Geometry (SIAGA),  member of the  editorial board

·         Journal of Symbolic Computation,  member of the editorial board

·         Mathematics in Computer Science,  member of the  editorial board

·         ACM Communications in Computer Algebra ,  member of the  editorial board (2012-2017)

·         Journal of System Science and Mathematical Science ,  member of the  editorial board

·         Symbolic and Numeric Computation, Special issue for Mathematics in Computer Science, guest editor

·         Symbolic-Numeric Computation,  Trends in Mathematics, guest editor

·         Proceedings of the 2014 International Symposium on Symbolic-Numeric Computation , co-editor
Teaching Experience

    Concrete Mathematics
    (1998, 1999, 2000, course for undergraduate students)
    The Internet for Scientists and Engineers
    (1999, course for undergraduate students)
    Basics in Technical English of Computer Science
    (1999, 2000, course for undergraduate students)
    Polynomial Algorithms in Computer Algebra
    (1998, 1999, 2000, course for graduate students)
    Modern Computer Algebra
    (2002, 2004 course for graduate students)
    Solving Polynomial System
    (2006 course for graduate students)


Research Statement

My research focuses on the development of techniques and algorithms in symbolic and numeric computations. Beginning with my doctoral research at the Institute of Systems Science, I have been working in the complementary areas of symbolic and numeric computations, including Ritt-Wu's Characteristic Set method, polynomial factorization over algebraic extension fields, parallelism in symbolic mathematical computations, numeric/symbolic hybrid algorithms for polynomials.

For further information about specific fields:
Symbolic/Numeric Hybrid Algorithms
Polynomial Factorization over Algebraic Extension Fields
Ritt-Wu's Characteristic Set Method


Go Back to Zhi's Home
lzhi@mmrc.iss.ac.cn


Zhi's Modest List of Publications
Papers Published in Journals and Books

    Kisun Lee and Nan Li and Lihong Zhi
    On isolation of singular zeros of multivariate analytic systems
    Journal of Symbolic Computation, 2019 (to appear). LeeLiZhi2020.pdf
    Zhiwei Hao and Wenrong Jiang and Nan Li and Lihong Zhi
    On Isolation of Simple Multiple Zeros and Clusters of Zeros of Polynomial Systems
    Mathematics of Computation, 89(322):879-909, 2020.
    HaoJiangLiZhi2020.pdf
    Mohab Safey El Din and Zhihong Yang and Lihong Zhi
    Computing Real Radicals and S-radicals of Polynomial Systems
    Journal of Symbolic Computation, 2019 (to appear).
    SafeyYangZhi2019.pdf
    Chu Wang and Lihong Zhi
    Lifts of Non-compact Convex Sets and Cone Factorizations
    Journal of Systems Science and Complexity 2019(to appear).
    WangZhi2019.pdf
    Chu Wang and Zhihong Yang and Lihong Zhi
    Global Optimization of Polynomials over Real Algebraic Sets
    Journal of Systems Science and Complexity 32:158-184, 2019.
    WangYangZhi2019.pdf
    Yue Ma and Chu Wang and Lihong Zhi
    A Certificate for Semidefinite Relaxations in Computing Positive-Dimensional Real Radical Ideals
    Journal of Symbolic Computation, 72:1-20, 2016.
    MaWangZhi2016.pdf
    Feng Guo and Chu Wang and Lihong Zhi
    Semidefinite Representations of Non-compact Convex Sets
    SIAM Journal on Optimization, 25(1):377-395, 2015.
    GuoWangZhi2015.pdf
    Nan Li and Lihong Zhi
    Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
    SIAM Journal on Numerical Analysis, 52(4):1623-1640, 2014.
    VMR.pdf
    Zijia Li and Lihong Zhi
    Computing the Nearest Singular Univariate Polynomials with Given Root Multiplicities
    Theoretical Computer Science 479:163-173, 2013.
    LiZijiaZhiTCS.pdf
    Nan Li and Lihong Zhi
    Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
    Theoretical Computer Science 479:150-162, 2013.
    LiZhiTCS.pdf
    Nan Li and Lihong Zhi
    Computing isolated singular solutions of polynomial systems: case of breadth one
    SIAM Journal on Numerical Analysis, 50(1):354-372, 2012.
    LiZhi2011revised.pdf
    Aurélien Greuet , Feng Guo, Mohab Safey El Din and Lihong Zhi
    Global optimization of polynomials restricted to a smooth variety using sums of squares
    Journal of Symbolic Computation, 47:503-518, 2012.
    Preliminary version sos_vcg_final.pdf
    Mohab Safey El Din and Lihong Zhi
    Computing rational points in convex semi-algebraic sets and sums of squares decompositions
    SIAM Journal on Optimization, 20(6):2876-2889, 2010.
    convex_sas.pdf
    Nan Li and Lihong Zhi
    Computing the multiplicity structure of an isolated singular solution: case of breadth one
    Journal of Symbolic Computation, 47(6):700-710, 2012.
    finalversionLIZHI.pdf
    Erich Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi
    Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
    Journal of Symbolic Computation, 47(1):1-15, 2012.
    KLYZ09.pdf
    Xiaoli Wu and Lihong Zhi
    Computing the multiplicity structure from geometric involutive form
    Journal of Symbolic Computation, 47(3):227-238, 2012.
    jsc_zhiwu.pdf
    Bin Li, Jiawang Nie,and Lihong Zhi
    Approximate GCDs of polynomials and sparse SOS relaxations.
    Theoretical Computer Science, 409(2) pp.200-210, 2008.
    LNZTCS08.pdf
    Greg Reid and Lihong Zhi
    Solving polynomials systems via symbolic-numeric eliminational method.
    Journal of Symbolic Computation, 44 pp.280-291, 2009.
    ReidZhiJSC08.pdf
    Erich Kaltofen, John P. May, Zhengfeng Yang, and Lihong Zhi
    Approximate factorization of multivariate polynomials using singular value decomposition.
    Journal of Symbolic Computation, 43(5) pp.359-376, 2008.
    KMYZJSC08.pdf
    Bingyu Li, Zhuojun Liu, and Lihong Zhi
    A Structured Rank-revealing Method for Sylvester Matrix
    Journal of Computational and Applied Mathematics,213 pp.212-223, 2008
    llzcam08.pdf
    Bingyu Li, Zhuojun Liu, and Lihong Zhi
    AFast Algorithm for Solving the Sylvester Structured TotalLeast Squares Problem
    Signal Processing, 87 (2007) pp.2313-2319.
    llzsp07.pdf
    Dongxia Sun and Lihong Zhi
    Structured Low Rank Approximation of a Bezout Matrix
    Mathematics in Computer Science, 2 (2007) pp.427-437.
    SunZhiMCS07.pdf
    Bingyu Li, Zhengfeng Yang, and Lihong Zhi
    Fast Low Rank Approximation of a Sylvester Matrix by Structure Total Least Norm
    Journal of Japan Society for Symbolic and Algebraic Computation, 11(3,4) (2005) pp.165-174.
    lyzjssac05.ps
    Robert M. Corless, Stephen M. Watt, and Lihong Zhi
    QR Factoring to Compute the GCD of Univariate Approximate Polynomials
    IEEE Transactions on Signal Processing, 52(12) pp.3394-3402, 2004.
    QRGCD.pdf
    Lihong Zhi, Matu-Tarow Noda, Hiroshi Kai, and Wenda Wu
    Hybrid Method for Computing the Nearest Singular Polynomials
    Japan Journal of Industrial and Applied Mathematics, 21(2) pp.149-162, June 2004.
    znkwjjiam04.pdf
    Lihong Zhi
    Hybrid Computation Lectures on Computer Algebra, (Ed. Dongming Wang, Lu Yang, Lihong Zhi, etc.), Tsing Hua Press, 2003.
    hybrid.pdf
    Lihong Zhi
    Algebraic Factorization and GCD Computation
    Mathematics Mechanization and Applications, (Ed. Xiao-Shan Gao and Dongming Wang), Academic Press, 2000, pp 325-342.
    mmfac.pdf
    K. Shiraishi H., Lihong Zhi, and Matu-Tarow Noda
    Implement of Wu's Method in Risa/Asir
    Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.41-42(abstract).
    H. Minaguchi, Lihong Zhi , Hiroshi Kai and Matu-Tarow Noda
    Apply General Inverse of Matrix to Compute Nearest Singular Polynomials
    Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.29-30(abstract).
    Lihong Zhi and Zhuojun Liu
    The P-irreducibility of Binding Polynomials
    An International Journal of Computers & Mathematics with Applications, 38(2) (1999) pp.1-10.
    pirr.pdf
    Lihong Zhi and Wenda Wu
    Nearest Singular Polynomials
    Journal of Symbolic Computation, 26(6) pp.667-676, December 1998.
    nsp.pdf
    Lihong Zhi
    An Optimal Method for Algebraic Factoring
    Journal of Computer Science and Technology, 12 pp. 1-9, January 1997.
    opfac.pdf

Papers Published in Conference Proceedings

    Mohab Safey El Din, Zhi-Hong Yang, and Lihong Zhi
    On the complexity of computing real radicals of polynomial
    In ISSAC'2018 Proc. 2018 Internat. Symp. Symbolic Algebraic Comput.
    SafeyYangZhi2018.pdf
    Dumas, Erich L. Kaltofen, Gilles Villard and Lihong Zhi
    Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits
    In ISSAC'2017 Proc. 2017 Internat. Symp. Symbolic Algebraic Comput.
    DKVZ2017.pdf
    Lihong Zhi
    Computing Multiple Zeros of Polynomial Systems: Case of Breadth One
    In CASC'2017 . International Workshop on Computer Algebra in Scientific Computing.
    Zhi2017.pdf
    Zhiwei Hao, Erich L. Kaltofen, and Lihong Zhi
    Numerical sparsity determination and early termination
    In ISSAC'2016 Proc. 2016 Internat. Symp. Symbolic Algebraic Comput.
    HKZ2016.pdf
    Feng Guo, Mohab Safey El Din, Chu Wang, and Lihong Zhi
    Optimizing a parameteric linear function over a non-compact real algebraic variety
    In ISSAC'2015 Proc. 2015 Internat. Symp. Symbolic Algebraic Comput.
    GSWZ2015.pdf
    Feng Guo, Chu Wang, and Lihong Zhi
    Optimizing a Linear Function over a Noncompact Real Algebraic Variety
    In SNC'2014 Proc. SNC Internat. Symp. Symbolic-Numeric Computation.
    GWZ2014SNC.pdf
    Qingdong Guo, Mohab Safey El Din, and Lihong Zhi
    Computing rational solutions of linear matrix inequalities
    In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
    GuoSafeyZhiISSAC2013.pdf
    Zhengfeng Yang, Lihong Zhi, and Yijun Zhu
    Verfied error bounds for real solutions of positive-dimensional polynomial systems
    In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
    YangZhiZhuISSAC2013.pdf

    Feng Guo, Erich Kaltofen, and Lihong Zhi
    Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions
    In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 195-202
    URL: http://arxiv.org/abs/1203.0253.

    Yue Ma and Lihong Zhi
    Computing Real Solutions of Polynomial Systems via Low-Rank Moment Matrix Completion In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 249-256
    MaZhiISSAC2012.pdf
    Yue Ma and Lihong Zhi
    The Minimum-Rank Gram Matrix Completion via Modified Fixed Point Continuation Method
    In ISSAC'2011 Proc. 2011 Internat. Symp. Symbolic Algebraic Comput. pp. 241-248
    MaZhiISSAC2011.pdf

    Sharon Hutton, Erich Kaltofen, and Lihong Zhi
    Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of seidenberg¡¯s method
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 227-234
    p227-hutton.pdf

    Zijia Li, Zhengfeng Yang, and Lihong Zhi
    Blind image deconvolution via fast approximate GCD
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 155-162
    55_paper.pdf
    Feng Guo, Mohab Safey El Din, and Lihong Zhi
    Global optimization of polynomials using generalized critical values and sums of squares
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 107-114
    p107-guo.pdf
    Xiaoli Wu and Lihong Zhi
    Computing the multiplicity structure from geometric involutive form
    In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 325-332
    WuZhiISS08.pdf
    Erich Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi
    Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars.
    In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 155-163
    KLYZISS08.pdf
    Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    On Probabilistic Analysis of Randomization in Hybrid Symbolic-Numeric Algorithms
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.   pp. 11-17
    KYZsnc07.pdf
    Erich Kaltofen, Bin Li, Kartik Sivaramakrishnan, Zhengfeng Yang, and Lihong Zhi
    Lower Bounds for Approximate Factorizations via Semidefinite Programming(extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.   pp. 203-204
    KLSYZsnc07.pdf
    Bin Li, Jiawang Nie, and Lihong Zhi
    Approximate GCDs of Polynomials and SOS Relaxation (extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-Numeric Comput.   pp. 205-206
    lnzsnc07.pdf
    Lihong Zhi
    Numerical Optimization in Hybrid Symbolic-numeric Computation (extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.pp. 33-35
    zhisnc07.pdf
    Erich Kaltofen and Lihong Zhi
    Hybrid Symbolic-numeric Computation
    In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 7
    KZiss06.pdf
    Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    Approximate Greatest Common Divisors of Several Polynomials with Linearly Constrained Coefficients and Singular Polynomials
    In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 169-176
    KYZiss06.pdf
    Bingyu Li , Zhuojun Liu, and Lihong Zhi
    A Structured Rank-revealing Method for Sylvester Matrix
    Conference on Applications of Computer Algebra, July 31-August 3, 2005
    Bingyu Li , Zhuojun Liu, and Lihong Zhi
    Fast Low Rank Approximation of a Sylvester Matrix
    In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 202-208, 2005
    LLZsnc05.ps
    Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    Structured Low Rank Approximation of a Sylvester Matrix
    In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 188-201, 2005
    KYZsnc05.ps
    Greg Reid and Lihong Zhi
    Solving Nonlinear Polynomial System via Symbolic-Numeric Elimination Method
    Proceedings of international conference on polynomial system solving£¬pp. 50-53£¬ 2004
    rzicpss04.pdf
    Greg Reid, Jianliang Tang, Jianping Yu, and Lihong Zhi
    Hybrid method for solving new pose estimation equation system
    Proceedings of the 2004 International Workshop on Computer and Geometric Algebra with Applications, LNCS 3519, H. Li et al. (eds), Springer Berlin Heidelberg, pp.46-57, 2005.
    rtyz04.pdf
    Shuhong Gao, Erich Kaltofen, John P. May, Zhengfeng Yang, and Lihong Zhi
    Approximate factorization of multivariate polynomials via differential equations.
    Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 167-174, 2004. ACM SIGSAM's ISSAC 2004 Distinguished Student Author Award (May and Yang).
    GKMYZ04.pdf
    Joe Bonasia, Francois Lemaire, Greg Reid, Robin Scott, and Lihong Zhi
    Determination of approximate symmetries of differential equations
    In Gomez-Ullate (ed.), CRM Proceedings and Lecture Notes 39: 233-249, Amer. Math. Soc, 2004.
    ApproxSym.pdf
    Lihong Zhi
    Displacement Structure in Computing the Approximate GCD of Univariate Polynomials
    Mathematics, pp.288-298, W.Sit and Z. Li(eds), World Scientific (Lecture Notes Series on Computing) 2003.
    displacement.pdf
    Greg Reid, Jianliang Tang, and Lihong Zhi
    A Complete Symoblic-Numeric Linear Method for Camera Pose Determination
    Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 215-223, 2003.
    trzissac03.pdf
    Lihong Zhi, M.-T Noda, and K. Li
    On the construction of PSE for GCD Computation
    Proceedings of the Asian Symposium on Computer Mathematics, pp.76-81, World Scientific (Lecture Notes Series on Computing) 2001.
    Kai Li, Lihong Zhi, and Matu-Tarow Noda
    Solving Approximate GCD of Multivariate Polynomials By Maple/Matlab/C Combination
    Proceedings of the Asian Technology Conference in Mathematics, pp.492-499, Chiangmai, Thailand, 2000.
    znlatcm00.pdf
    Lihong Zhi and M.-T. Noda
    Approximate GCD of Multivariate Polynomials
    Proceedings of the Asian Symposium on Computer Mathematics, pp.9-18, Chiangmai, Thailand, 2000.
    znascm00.pdf
    Yuzhen Huang, H.J.Stetter , Wenda Wu, and Lihong Zhi
    Pseudofactors of Multivariate Polynomials
    Proceedings of the 2000 International Symposium on Symoblic and Algebraic Compuation, pp.161-168. St. Andrews United Kingdom, 2000.
    HSWZISS00.ps
    Lihong Zhi , Y. Notake, H. Kai, and M.-T. Noda
    Hybrid Method for Solving Polynomial Equations
    Proceedings of the Asian Technology Conference in Mathematics, pp.492-501, Guangzhou, China, 1999.
    atcm99.pdf
    Lihong Zhi and Wenda Wu
    Nearest Singular Polynomials I
    Proceedings of the Asian Technology Conference in Mathematics, pp.323-332, Tsukuba, Japan, 1998.
    Dongming Wang and Lihong Zhi
    Algebraic Factorization Applied to Geometric Problems
    Proceedings of the Asian Symposium on Computer Mathematics, pp.23-36, Lan Zhou, China, 1998.
    zwfac.pdf
    Lihong Zhi and Wenda Wu
    A Note on Small Perturbations to Polynomials(abstract)
    Proceedings of the Asian Technology Conference in Mathematics, Penang, Malaysia, 1997.
    Kai Huang, Dingkang Wang, and Lihong Zhi
    Wu method and its Applications (abstract)
    Proceedings of the Asian Technology Conference in Mathematics, Penang, Malaysia, 1997.
    hwzatcm97.pdf
    Dingkang Wang and Lihong Zhi
    Software Development in MMRC
    Proceedings of the Asian Technology Conference in Mathematics, Singapore, December 18-21, 1995, pp 234-243.
    sdmmrc.pdf

Posters

    R. Corless, S. Watt, and Lihong Zhi
    QR Factorization for Computing Approximate GCD
    The 2002 International Symposium on Symbolic and Algebraic Computation, 2002.
    Iyad A. Ajwa and Lihong Zhi
    CharSets: An Efficient Implementation of the Characteristic Sets Method
    The Fifth Annual East Coast Computer Algebra Day, ECCAD '98, United States Naval Academy, Annapolis, Maryland, April 25, 1998.

Technical Reports
Dissertation

    Lihong Zhi
    Polynomial Factorization over Algebraic Fields and its Applications
    Ph.D. Dissertation, Institute of Systems Science, Academia Sinica, Beijing, China, July 1996.


Go Back to Zhi's Home
lzhi@mmrc.iss.ac.cn



Current Classes

    Concrete Mathematics
    Syllabus
    Assignments
    Polynomial Algorithms in Computer Algebra
    Syllabus
    Assignments
    Modern Computer Algebra
    Ziming Li's Lecture Notes
    Syllabus
    Assignments



Go Back to Zhi's Home
lzhi@mmrc.iss.ac.cn