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Xia, Bican

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Author ID: xia.bican Recent zbMATH articles by "Xia, Bican"
Published as: Xia, Bican; Xia, BiCan; Xia, B. C.
Documents Indexed: 56 Publications since 1998, including 1 Book

Publications by Year

Citations contained in zbMATH Open

39 Publications have been cited 227 times in 138 Documents Cited by Year
A complete algorithm for automated discovering of a class of inequality-type theorems. Zbl 1125.68406
Yang, Lu; Hou, Xiaorong; Xia, Bican
24
2001
An algorithm for isolating the real solutions of semi-algebraic systems. Zbl 1027.68150
Xia, Bican; Yang, Lu
23
2002
Computing cylindrical algebraic decomposition via triangular decomposition. Zbl 1237.14068
Chen, Changbo; Moreno Maza, Marc; Xia, Bican; Yang, Lu
21
2009
Stability analysis of biological systems with real solution classification. Zbl 1360.92048
Wang, Dongming; Xia, Bican
14
2005
Real solution isolation using interval arithmetic. Zbl 1131.65041
Xia, Bican; Zhang, Ting
12
2006
Triangular decomposition of semi-algebraic systems. Zbl 1260.14070
Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong
11
2013
A complete algorithm for counting real solutions of polynomial systems of equations and inequalities. Zbl 1035.65054
Xia, Bican; Hou, Xiaorong
10
2002
Constructing fewer open cells by GCD computation in CAD projection. Zbl 1325.68286
Han, Jingjun; Dai, Liyun; Xia, Bican
10
2014
Discovering non-linear ranking functions by solving semi-algebraic systems. Zbl 1147.68442
Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun; Zhou, Chaochen
8
2007
Triangular decomposition of semi-algebraic systems. Zbl 1321.68526
Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong
8
2010
Discovering polynomial Lyapunov functions for continuous dynamical systems. Zbl 1338.37025
She, Zhikun; Li, Haoyang; Xue, Bai; Zheng, Zhiming; Xia, Bican
8
2013
Generating polynomial invariants with DISCOVERER and QEPCAD. Zbl 1151.68366
Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun
7
2007
A semi-algebraic approach for asymptotic stability analysis. Zbl 1217.93153
She, Zhikun; Xia, Bican; Xiao, Rong; Zheng, Zhiming
7
2009
Recent advances in program verification through computer algebra. Zbl 1267.68099
Yang, Lu; Zhou, Chaochen; Zhan, Naijun; Xia, Bican
6
2010
Termination of linear programs with nonlinear constraints. Zbl 1208.68151
Xia, Bican; Zhang, Zhihai
5
2010
Barrier certificates revisited. Zbl 1357.68110
Dai, Liyun; Gan, Ting; Xia, Bican; Zhan, Naijun
5
2017
Automated discovering and proving for geometric inequalities. Zbl 0947.03017
Yang, Lu; Hou, Xiaorong; Xia, Bican
5
1999
Symbolic decision procedure for termination of linear programs. Zbl 1216.68077
Xia, Bican; Yang, Lu; Zhan, Naijun; Zhang, Zhihai
5
2011
Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029
Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong
3
2011
Real root isolation of polynomial equations based on hybrid computation. Zbl 1336.65080
Shen, Fei; Wu, Wenyuan; Xia, Bican
3
2014
Proving inequalities and solving global optimization problems via simplified CAD projection. Zbl 1337.90052
Han, Jingjun; Jin, Zhi; Xia, Bican
3
2016
Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021
Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong
3
2013
On solving parametric polynomial systems. Zbl 1274.13047
Maza, Marc Moreno; Xia, Bican; Xiao, Rong
3
2012
Automated inequality proving and discovering. Zbl 1362.26001
Xia, Bican; Yang, Lu
2
2016
Special algorithm for stability analysis of multistable biological regulatory systems. Zbl 1328.92028
Hong, Hoon; Tang, Xiaoxian; Xia, Bican
2
2015
Some properties of the discrimination matrix of polynomials with applications. Zbl 1051.15010
Xia, Bican; Yang, Lu
2
2003
A new sparse SOS decomposition algorithm based on term sparsity. Zbl 1467.68234
Wang, Jie; Li, Haokun; Xia, Bican
2
2019
Condition number based complexity estimate for solving polynomial systems. Zbl 1211.65059
She, Zhikun; Xia, Bican; Zheng, Zhiming
2
2011
Generic regular decompositions for parametric polynomial systems. Zbl 1327.93101
Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican
2
2015
Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems. Zbl 1420.68244
Wang, Qiuye; Li, Yangjia; Xia, Bican; Zhan, Naijun
2
2017
Automated deduction in real geometry. Zbl 1082.65054
Yang, Lu; Xia, Bican
1
2004
A new method for real root isolation of univariate polynomials. Zbl 1132.68074
Zhang, Ting; Xia, Bican
1
2007
A special homotopy continuation method for a class of polynomial systems. Zbl 1455.65079
Wang, Yu; Wu, Wenyuan; Xia, Bican
1
2017
Interpolant synthesis for quadratic polynomial inequalities and combination with EUF. Zbl 06623262
Gan, Ting; Dai, Liyun; Xia, Bican; Zhan, Naijun; Kapur, Deepak; Chen, Mingshuai
1
2016
Real solution isolation with multiplicity of zero-dimensional triangular systems. Zbl 1218.65046
Zhang, ZhiHai; Fang, Tian; Xia, BiCan
1
2011
Open weak CAD and its applications. Zbl 1410.68410
Han, Jingjun; Dai, Liyun; Hong, Hoon; Xia, Bican
1
2017
An effective framework for constructing exponent lattice basis of nonzero algebraic numbers. Zbl 1462.11113
Zheng, Tao; Xia, Bican
1
2019
Solution to the generalized champagne problem on simultaneous stabilization of linear systems. Zbl 1124.93030
Guan, Qiang; Wang, Long; Xia, Bican; Yang, Lu; Yu, Wensheng; Zeng, Zhenbing
1
2007
Decidability of the reachability for a family of linear vector fields. Zbl 06527570
Gan, Ting; Chen, Mingshuai; Dai, Liyun; Xia, Bican; Zhan, Naijun
1
2015
A new sparse SOS decomposition algorithm based on term sparsity. Zbl 1467.68234
Wang, Jie; Li, Haokun; Xia, Bican
2
2019
An effective framework for constructing exponent lattice basis of nonzero algebraic numbers. Zbl 1462.11113
Zheng, Tao; Xia, Bican
1
2019
Barrier certificates revisited. Zbl 1357.68110
Dai, Liyun; Gan, Ting; Xia, Bican; Zhan, Naijun
5
2017
Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems. Zbl 1420.68244
Wang, Qiuye; Li, Yangjia; Xia, Bican; Zhan, Naijun
2
2017
A special homotopy continuation method for a class of polynomial systems. Zbl 1455.65079
Wang, Yu; Wu, Wenyuan; Xia, Bican
1
2017
Open weak CAD and its applications. Zbl 1410.68410
Han, Jingjun; Dai, Liyun; Hong, Hoon; Xia, Bican
1
2017
Proving inequalities and solving global optimization problems via simplified CAD projection. Zbl 1337.90052
Han, Jingjun; Jin, Zhi; Xia, Bican
3
2016
Automated inequality proving and discovering. Zbl 1362.26001
Xia, Bican; Yang, Lu
2
2016
Interpolant synthesis for quadratic polynomial inequalities and combination with EUF. Zbl 06623262
Gan, Ting; Dai, Liyun; Xia, Bican; Zhan, Naijun; Kapur, Deepak; Chen, Mingshuai
1
2016
Special algorithm for stability analysis of multistable biological regulatory systems. Zbl 1328.92028
Hong, Hoon; Tang, Xiaoxian; Xia, Bican
2
2015
Generic regular decompositions for parametric polynomial systems. Zbl 1327.93101
Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican
2
2015
Decidability of the reachability for a family of linear vector fields. Zbl 06527570
Gan, Ting; Chen, Mingshuai; Dai, Liyun; Xia, Bican; Zhan, Naijun
1
2015
Constructing fewer open cells by GCD computation in CAD projection. Zbl 1325.68286
Han, Jingjun; Dai, Liyun; Xia, Bican
10
2014
Real root isolation of polynomial equations based on hybrid computation. Zbl 1336.65080
Shen, Fei; Wu, Wenyuan; Xia, Bican
3
2014
Triangular decomposition of semi-algebraic systems. Zbl 1260.14070
Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong
11
2013
Discovering polynomial Lyapunov functions for continuous dynamical systems. Zbl 1338.37025
She, Zhikun; Li, Haoyang; Xue, Bai; Zheng, Zhiming; Xia, Bican
8
2013
Computing with semi-algebraic sets: relaxation techniques and effective boundaries. Zbl 1277.13021
Chen, Changbo; Davenport, James H.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong
3
2013
On solving parametric polynomial systems. Zbl 1274.13047
Maza, Marc Moreno; Xia, Bican; Xiao, Rong
3
2012
Symbolic decision procedure for termination of linear programs. Zbl 1216.68077
Xia, Bican; Yang, Lu; Zhan, Naijun; Zhang, Zhihai
5
2011
Computing with semi-algebraic sets represented by triangular decomposition. Zbl 1323.14029
Chen, Changbo; Davenport, James H.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong
3
2011
Condition number based complexity estimate for solving polynomial systems. Zbl 1211.65059
She, Zhikun; Xia, Bican; Zheng, Zhiming
2
2011
Real solution isolation with multiplicity of zero-dimensional triangular systems. Zbl 1218.65046
Zhang, ZhiHai; Fang, Tian; Xia, BiCan
1
2011
Triangular decomposition of semi-algebraic systems. Zbl 1321.68526
Chen, Changbo; Davenport, James H.; May, John P.; Maza, Marc Moreno; Xia, Bican; Xiao, Rong
8
2010
Recent advances in program verification through computer algebra. Zbl 1267.68099
Yang, Lu; Zhou, Chaochen; Zhan, Naijun; Xia, Bican
6
2010
Termination of linear programs with nonlinear constraints. Zbl 1208.68151
Xia, Bican; Zhang, Zhihai
5
2010
Computing cylindrical algebraic decomposition via triangular decomposition. Zbl 1237.14068
Chen, Changbo; Moreno Maza, Marc; Xia, Bican; Yang, Lu
21
2009
A semi-algebraic approach for asymptotic stability analysis. Zbl 1217.93153
She, Zhikun; Xia, Bican; Xiao, Rong; Zheng, Zhiming
7
2009
Discovering non-linear ranking functions by solving semi-algebraic systems. Zbl 1147.68442
Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun; Zhou, Chaochen
8
2007
Generating polynomial invariants with DISCOVERER and QEPCAD. Zbl 1151.68366
Chen, Yinghua; Xia, Bican; Yang, Lu; Zhan, Naijun
7
2007
A new method for real root isolation of univariate polynomials. Zbl 1132.68074
Zhang, Ting; Xia, Bican
1
2007
Solution to the generalized champagne problem on simultaneous stabilization of linear systems. Zbl 1124.93030
Guan, Qiang; Wang, Long; Xia, Bican; Yang, Lu; Yu, Wensheng; Zeng, Zhenbing
1
2007
Real solution isolation using interval arithmetic. Zbl 1131.65041
Xia, Bican; Zhang, Ting
12
2006
Stability analysis of biological systems with real solution classification. Zbl 1360.92048
Wang, Dongming; Xia, Bican
14
2005
Automated deduction in real geometry. Zbl 1082.65054
Yang, Lu; Xia, Bican
1
2004
Some properties of the discrimination matrix of polynomials with applications. Zbl 1051.15010
Xia, Bican; Yang, Lu
2
2003
An algorithm for isolating the real solutions of semi-algebraic systems. Zbl 1027.68150
Xia, Bican; Yang, Lu
23
2002
A complete algorithm for counting real solutions of polynomial systems of equations and inequalities. Zbl 1035.65054
Xia, Bican; Hou, Xiaorong
10
2002
A complete algorithm for automated discovering of a class of inequality-type theorems. Zbl 1125.68406
Yang, Lu; Hou, Xiaorong; Xia, Bican
24
2001
Automated discovering and proving for geometric inequalities. Zbl 0947.03017
Yang, Lu; Hou, Xiaorong; Xia, Bican
5
1999
all top 5

Cited by 220 Authors

23 Xia, Bican
11 Davenport, James Harold
11 England, Matthew
8 Moreno Maza, Marc
8 She, Zhikun
7 Chen, Changbo
7 Zhan, Naijun
6 Tang, Xiaoxian
5 Bradford, Russell J.
5 Wang, Dongming
5 Wilson, David J.
5 Yang, Lu
5 Zhang, Zhihai
5 Zhao, Hengjun
4 Dai, Liyun
4 Feng, Yong
4 Gao, Xiaoshan
4 Niu, Wei
4 Wu, Wenyuan
4 Zheng, Zhiming
3 Boulier, François
3 Han, Jingjun
3 Huang, Bo
3 Kapur, Deepak
3 Lai, Yisheng
3 Lemaire, François
3 Sun, Xianbo
3 Wang, Jihua
3 Wang, Renhong
3 Wu, Jinming
3 Xu, Ming
3 Yang, Zhengfeng
3 Yu, Pei
3 Zeng, Zhenbing
3 Zhi, Lihong
2 Ábrahám, Erika
2 Bridge, James P.
2 Chen, Zhenghong
2 Cheng, Jinsan
2 Giesl, Peter
2 Hafstein, Sigurður Freyr
2 Hong, Hoon
2 Hou, Xiaorong
2 Huang, Chengchao
2 Huang, Zongyan
2 Jiang, Xin
2 Kazemi, Mahsa
2 Lasserre, Jean-Bernard
2 Li, Xiaoliang
2 Li, Zhibin
2 Lichtblau, Daniel A.
2 Lin, Wang
2 Liu, Jiang
2 Lu, Junjie
2 Magron, Victor
2 Paulson, Lawrence Charles
2 Poteaux, Adrien
2 Seiler, Werner M.
2 Strzeboński, Adam Wojciech
2 Wang, Chu
2 Wang, Long
2 Weber, Andreas Günter
2 Xiao, Rong
2 Yang, Zhihong
2 Yap, Chee-Keng
2 Yu, Wensheng
2 Zhang, Jingzhong
1 Abánades, Miguel Angel
1 Abbott, John A.
1 Abdel-Rahman, Essam Othman
1 Alvandi, Parisa
1 Ataei, Masoud
1 Becker, Bernd
1 Bigatti, Anna Maria
1 Botana, Francisco
1 Brain, Martin
1 Brown, Christopher W.
1 Buchberger, Bruno
1 Chen, Jingwei
1 Chen, Michael Z. Q.
1 Chen, Mingshuai
1 Chen, Shikun
1 Chen, Shiping
1 Chen, Taolue
1 Chen, Xiaoyu
1 Chen, Zhanbo
1 Cimatti, Alessandro
1 Corless, Robert Malcolm
1 Dai, Yanfei
1 Dixit, Atul
1 Dreisigmeyer, David W.
1 Errami, Hassan
1 Fan, Zhe
1 Fang, Tian
1 Ferragut, Antoni
1 Fontaine, Pascal
1 Forrest, Stephen
1 Gan, Ting
1 García-Saldaña, Johanna D.
1 Gasull, Armengol
...and 120 more Authors
all top 5

Cited in 43 Serials

27 Journal of Symbolic Computation
17 Journal of Systems Science and Complexity
10 Mathematics in Computer Science
6 Computers & Mathematics with Applications
5 Journal of Computational and Applied Mathematics
5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
4 Discrete and Continuous Dynamical Systems. Series B
3 Formal Aspects of Computing
3 Science China. Information Sciences
2 Chaos, Solitons and Fractals
2 Applied Mathematics and Computation
2 Automatica
2 Theoretical Computer Science
2 Science in China. Series A
2 SIAM Journal on Optimization
2 SIAM Journal on Applied Dynamical Systems
2 Nonlinear Analysis. Hybrid Systems
1 International Journal of Systems Science
1 Journal of Mathematical Analysis and Applications
1 Bulletin of Mathematical Biology
1 Journal of Mathematical Economics
1 Journal of Optimization Theory and Applications
1 SIAM Journal on Control and Optimization
1 Systems & Control Letters
1 Journal of Automated Reasoning
1 Computational Geometry
1 Journal of Global Optimization
1 International Journal of Computer Mathematics
1 Journal of Nonlinear Science
1 Computational Complexity
1 Bulletin des Sciences Mathématiques
1 Journal of Difference Equations and Applications
1 Abstract and Applied Analysis
1 Annals of Combinatorics
1 Chaos
1 Acta Mathematica Sinica. English Series
1 Communications in Nonlinear Science and Numerical Simulation
1 Qualitative Theory of Dynamical Systems
1 Journal of the Australian Mathematical Society
1 Science in China. Series F
1 Frontiers of Computer Science in China
1 Frontiers of Computer Science
1 International Journal of Systems Science. Principles and Applications of Systems and Integration

Citations by Year