Seak Weng VONG, George黃錫榮
Associate Professor

Academic Qualifications | Working Experience | Teaching | Professional Services | Research | Selected Publications | Master Student | PhD Student | Contact Details

Academic Qualification

  • Ph.D. in Mathematics, City University of Hong Kong (2005)
  • M.Sc. in Mathematics, University of Macau (2000)
  • B.Ed. in Mathematics, University of Macau (1996)

Working Experience

1996-2000   Teaching Assistant, Faculty of Science and Technology, University of Macau.
2000-2005   Lecturer, Faculty of Science and Technology, University of Macau.
2005-2012   Assistant Professor, Faculty of Science and Technology, University of Macau.
2012-now   Associate Professor, Faculty of Science and Technology, University of Macau.

Teaching

B.Sc. Courses

  1. Probability and Statistics (MATH111)
  2. Operations Research I (SFTW122)
  3. Operations Research II (SFTW221)
  4. Calculus II (MATB120)
  5. Complex Analysis (MATB311)
  6. Real Analysis II
  7. Discrete Mathematics

M.Sc. Courses

  1. Partial Differential Equations (IMAT010)
  2. Advanced Engineering Mathematics

Professional Services

  • Member of Executive Committee of SIAM – East Asia Section
  • Secretary of SIAM – East Asia Section (2017-2018)
  • Reviewer for Mathematical Review (American Mathematical Society)
  • Editor of Numerical Algebra, Control and Optimization (Scopus)
  • Serve as a guest editor for the following  issues of SCIE journals:
    • Vol 4 (1), East Asian Journal on Applied Mathematics
    • Vol 7 (4), East Asian Journal on Applied Mathematics
    • Vol 11(4), Numerical Mathematics: Theory, Methods and Applications

Research

Information to master student in mathematics: Research assistantship (2019/2020) of my grant is now open for application. Interested student can contact me for more details.
Link to Google Scholar: https://scholar.google.com/citations?user=egECINMAAAAJ&hl=zh-TW&oi=ao

Research Interests

  • Computational Linear and Multilinear Algebra
  • Hyperbolic Conservation Laws
  • Numerical method for partial differential equations

Awards

2016 Macao Natural Science Award from FDCT (second prize), X. Jin, S. Vong, C. Cheng
Title: Preconditioning techniques for Toeplitz systems with applications
2017 Long service awards (20 years of service)

Recent Research Projects (Since 2002 – present)

  • “Iterative Methods for Solving Inverse Eigenvalue Problems”, Grant no. MYRG062(Y1-L1)-FST11-VSW, from University of Macau.
  • “Positive Solutions to the Boundary Value Problems of Differential Equations”, Grant no. MYRG086(Y1-L2)-FST12-VSW, from University of Macau.
  • “High order compact schemes of partial differential equations”, Grant no. FDCT/001/2013/A, from FDCT
  • “High order numerical methods of partial differential equations” Grant no. MYRG2015-00064-FST, from University of Macau
  • “High order schemes of fractional differential equations”, Gran no. 010/2015/A, from FDCT
  • “Linearized methods of nonlinear fractional differential equations and related problems” Grant no. 050/2017/A, from FDCT
  • “Efficient numerical methods for fractional differential equations and tensor analysis” Grant no. MYRG2017-00098-FST, from University of Macau

Selected Publications

(“**” denotes top 5% (or above) ranking journals according to JCR@2018)
(“*” denotes top 10% (or above) ranking journals according to JCR@2018)

Journal Papers

Paper indexed by Web of Science:

Before 2012:

  1. *S. Vong, T. Yang & C. Zhu (2003). Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum (II), Journal of Differential Equations, Vol. 192, pp. 475-501. [Rank=19/313≈6% @Mathematics]
  2. *S. Vong (2006). The Boltzmann equation with frictional force, Journal of Differential Equations, Vol. 222, pp. 95-136. [Rank=19/313≈6% @Mathematics]
  3. L. Lin & S. Vong (2006).  A note on the existence and nonexistence of globally bounded classical solutions for nonisentropic gas, Acta Mathematica Scientia, Vol. 26B,  No. 3, pp. 537-540.
  4. C. Cheng, X. Jin, S. Vong & W. Wang (2007). A note on spectra of optimal and superoptimal preconditioned matrices, Linear Algebra Appl. 422, 482-485.
  5. S. Vong & X. Jin (2007). Unitarily Invariant Norms of Toeplitz Matrices with Fisher-Hartwig Singularities, SIAM J. Matrix Anal. Vol. 29, No. 3, pp. 850–854.
  6. S. Vong, W. Wang & X. Jin (2008). Convergence Analysis of Superoptimal PCG Algorithm for Toeplitz Sys ems with a Fisher-Hartwig Singularity, Linear Algebra Appl., Vol. 428, pp. 535-549.
  7. S. Vong and X. Jin (2008), Proof of Bottcher and Wenzel’s Conjecture, Operators and Matrices, Vol. 2, pp. 435-442.
  8. C. Cheng, S. Vong, and D.Wenzel (2010), Commutators with maximal Frobenius norm, Linear Algebra Appl., 432, pp. 292-306.
  9. H. Pang, Y. Zhang, S. Vong, X. Jin (2011), Circulant preconditioners for pricing options, Linear Algebra Appl., Vol. 434, pp. 2325-2342.
  10. S. Vong, Z. Bai, and X. Jin (2011), A Ulm-like Method for Inverse Singular Value Problems, SIAM J. Matrix Anal. Appl., 32, pp. 412-429, 2011.
  11. **S. Vong (2011), On a generalization of Aczel’s inequality, Appl. Math. Lett., 24, pp. 1301-1307, 2011. [Rank=9/254≈4% @Mathematics, applied]
  12. *S. Vong (2011), A note on some Ostrowski-like type inequalities, Computers and Mathematics with Applications, 62, pp. 532-535, 2011. [Rank=18/254≈7% @Mathematics, applied]
  13. S. Vong, H. Pang, X. Jin, A high-order difference scheme for the generalized Cattaneo equation, East Asian J. Appl. Math., 2 (2012) 170-184.

2013:

  1. **Z. Wang^, S. Vong, On some Ostrowski-like type inequalities involving n knots, Appl. Math. Lett., 26 (2013), 296–300. . [Rank=9/254≈4% @Mathematics, applied]
  2. S. Vong, Q. Meng, S. Lei, On a discrete-time collocation method for the nonlinear Schrödinger equation with wave operator, Numer. Meth. Part. Diff. Equ., 29 (2013), 693–705.
  3. S. Vong, Positive solutions of singular fractional differential equations with integral boundary conditions, Mathematical and Computer Modelling 57 (2013), 1053–1059.
  4. Z. Wang^, S. Vong, A Gauss-Newton-like Method for Inverse Eigenvalue Problems, Int. J. Comput. Math., 90(7) (2013), 1435–1447.

2014:

  1. *Z. Wang^, S. Vong, On some generalizations of an Ostrowski-Gruss type integral inequality, Appl. Math. Comput., 229 (2014), 239–244.[Rank=14/254≈6% @Mathematics, applied]
  2. S. Vong, Z. Wang^, Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System, Adv. Appl. Math. Mech., 6(4) (2014), 419—435.
  3. W. Li, S. Vong, X. Peng, On eigenvalue perturbation bounds for Hermitian block tridiagonal matrices, Appl. Numer. Math., 83 (2014), 38–50.
  4. S. Vong, X. Jin, and J. Wang, The mediating morphism of the multilinear optimal map, East Asian J. Appl. Math.,  4 (2014), 82–87.
  5. *Z. Wang^, S. Vong, A high-order exponential ADI scheme for two dimensional time fractional convection-diffusion equations, Comput. Math. Appl., 68(3) (2014), 185–196. [Rank=18/254≈7% @Mathematics, applied]
  6. *S. Vong, Z. Wang^, A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions. J. Comput. Phys., 274 (2014), 268–282. [Rank=4/55≈7% @ Physics, Mathematical]
  7. S. Vong, Z. Wang^, High order difference schemes for a time fractional differential equation with Neumann boundary conditions, East Asian J. Appl. Math., 4(3) (2014), 222–241.
  8. *Z. Wang^, S. Vong, Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation. J. Comput. Phys., 277 (2014), 1–15. [Rank=4/55≈7% @ Physics, Mathematical]
  9. W. Qu, S. Lei, S. Vong ,Circulant and skew-circulant splitting iteration for fractional advection-diffusion equations. Int. J. Comput. Math., 91(10) (2014), 2232–2242.

2015:

  1. Z. Wang^, S. Vong, A high order ADI scheme for the two-dimensional time fractional diffusion-wave equation, Int. J. Comput. Math., 92(5) (2015), 970—997.
  2. **S. Vong, Z. Wang^, A high order compact finite difference scheme for time fractional Fokker-Planck equations. Appl. Math. Lett., 43  (2015), 38–43. [Rank=9/254≈4%  @Mathematics, applied]
  3. S. Vong, Z. Wang^, A high-order compact scheme for the nonlinear fractional Klein-Gordon equation. Numer. Meth. Part. Diff. Equ., 31(2015), no. 3, 706–722.
  4. H. Fok^, S. Vong, Generalizations of some Hermite-Hadamard-type inequalities. Indian J. Pure Appl. Math.  46  (2015),  no. 3, 359–370.
  5. S. Vong, Z. Wang^, A compact ADI scheme for the two dimensional time fractional diffusion-wave equation in polar coordinates, Numer. Meth. Part. Diff. Equ.,  31(5) (2015), 1692–1712.
  6. W. Li, D. Liu, S. Vong, Z-eigenpair bounds for an irreducible nonnegative tensor, Linear Algebra Appl.,  483  (2015), 182–199.
  7. C. Cheng, X. Jin, S. Vong, A survey on the Böttcher-Wenzel conjecture and related problems, Oper. Matrices,  9(3)  (2015) , 659–673.
  8. *T. Chen, W. Li, X. Wu, S. Vong, Error bounds for linear complementarity problems of MB -matrices. Numer. Algor. , 70(2)  (2015), 341–356. [Rank=24/254≈9%  @Mathematics, applied]

2016:

  1. *W. Li, Z. Xie, S. Vong, Sensitivity analysis for the symplectic QR factorization. J. Franklin Inst.  353(5)  (2016), 1186–1205. [Rank=7/105≈7% @ Mathematics, interdisciplinary appliactions]
  2. *S. Vong, P. Lyu^, Z. Wang^, A compact difference scheme for fractional sub-diffusion equations with the spatially variable coefficient under Neumann boundary conditions. J. Sci. Comput.  66(2)  (2016), 725–739. [Rank=26/254≈10%  @Mathematics, applied]
  3. Z. Wang^, S. Vong, S. Lei, Finite difference schemes for two-dimensional time-space fractional differential equations. Int. J. Comput. Math., 93(3)  (2016), 578–595.
  4. *S. Vong, P. Lyu^, X. Chen, S.L. Lei, High order finite difference method for time-space fractional differential equations with Caputo and Riemann-Liouville derivatives, Numer. Algor., 72 (2016), 195–210. [Rank=24/254≈9%  @Mathematics, applied]
  5. *Z. Wang^, S. Vong, A compact difference scheme for a two dimensional nonlinear fractional Klein–Gordon equation in polar coordinates, Comput. Math. Appl., 71(12) (2016),  2524–2540. [Rank=18/254≈7% @Mathematics, applied]
  6. L. Guo^, Z. Wang^, S. Vong, Fully discrete local discontinuous Galerkin methods for some time-fractional fourth-order problems, Int. J. Comput. Math., 93(10) (2016), 1665–1682.

2017:

  1. *H.L. Liao, P. Lyu^, S. Vong, Y. Zhao, Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations, Numer. Algor., 75(4) (2017), 845—878. [Rank=24/254≈9%  @Mathematics, applied]
  2. *H. Zheng, W. Li, S. Vong, A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems, Numer. Algor., 74 (2017), 137–152. [Rank=24/254≈9%  @Mathematics, applied]
  3. **S. Vong, P. Lyu^, On numerical contour integral method for fractional diffusion equations with variable coefficients, Appl. Math. Lett., 64 (2017), 137–142. [Rank=9/254≈4% @Mathematics, applied]
  4. **W. Li, S. Vong, On the variation of the spectrum of a Hermitian matrix, Appl. Math. Lett.,  65 (2017), 70–76. Rank=9/254≈4% @Mathematics, applied]
  5. W. Li, D. Liu^, M. Ng, S. Vong, The uniqueness of multilinear PageRank vectors, Numer. Linear Algebra Appl., (2017), DOI: 10.1002/nla.2107
  6. H. Zheng, S. Vong, W. Li, On perturbation bounds of the linear complementarity problem, Linear and Multilinear Algebra, (2017), http://dx.doi.org/10.1080/03081087.2017.1312682
  7. H.L. Liao, P. Lyu^, S. Vong, Second-order BDF time approximation for Riesz space-fractional diffusion equations, Int. J. Comput. Math., DOI: 10.1080/00207160.20171366461
  8. S. Vong, C.Y. Shi^, P. Lyu^, High-order compact schemes for fractional differential equations with mixed derivatives, Numer. Meth. Part. Diff. Equ., DOI: 10.1002/NUM.22183.
  9. *P. Lyu^, S. Vong, A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations, Numer. Algor., https://doi.org/10.1007/s11075-017-0385-y  [Rank=24/254≈9%  @Mathematics, applied]
  10. D. Liu^, W. Li, S. Vong, The tensor splitting with application to solve multi-linear systems, J. Comput. Appl. Math., https://doi.org/10.1016/j.cam.2017.08.009
  11. D. Liu^, W. Li, S. Vong, Tensor complementarity problems: the GUS-property and an algorithm, Linear and Multilinear Algebra, https://doi.org/10.1080/03081087.2017.1369929
  12. X. Lu, H.-K. Pang, H.-W. Sun, S. Vong, Approximate inversion method for time-fractional sub-diffusion equations, to appear in Numer. Linear Algebra Appl.

2018:

  1. **P. Lyu^, S. Vong, linearized second-order fnite difference scheme for time fractional generalized BBM equation, Applied Mathematics Letters, 78 (2018) 16–23 [Rank=9/252≈4% @Mathematics, applied]
  2. P. Lyu^, S. Vong, Z. Wang, A Finite Difference Method for Boundary Value Problems of a Caputo Fractional Differential Equation, East Asian Journal on Applied Mathematics, Vol. 7, No. 4, 752-766
  3. W. Li, W. Liu, S Vong, Some bounds for H-eigenpairs and Z-eigenpairs of a tensor, Journal of Computational and Applied Mathematics, 342 (2018), 37–57
  4. *W. Li, Y. Chen, S. Vong, Q. Luo, Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse, Numerical Algorithms, https://doi.org/10.1007/s11075-018-0473-7  [Rank=24/254≈9%  @Mathematics, applied]
  5. *X.-S. Chen, S. Vong, W. Li, H. Xu, Noda iterations for generalized eigenproblems following Perron-Frobenius theory, Numerical Algorithms, https://doi.org/10.1007/s11075-018-0512-4  [Rank=24/254≈9%  @Mathematics, applied]
  6. *S. Vong, P. Lyu^, Unconditional Convergence in Maximum-Norm of a Second-Order Linearized Scheme for a Time-Fractional Burgers-Type Equation, Journal of Scientific Computing, https://doi.org/10.1007/s10915-018-0659-0  [Rank=26/254≈10%  @Mathematics, applied]
  7. P. Lyu^,  S. Vong, A linearized and second-order unconditionally convergent scheme for coupled time fractional Klein-Gordon-Schrödinger equation, Numerical Methods for Partial Differential Equations, https://doi.org/10.1002/num.22282
  8. S. Vong, D. Liu^, An inertial Mann algorithm for nonexpansive mappings, Journal of Fixed Point Theory Appl. (2018) 20: 102. https://doi.org/10.1007/s11784-018-0583-9
  9. H. Zheng, S. Vong, Improved convergence theorems of the two-step modulus-based matrix splitting and synchronous multisplitting iteration methods for solving linear, Linear and Multilinear Algebra, https://doi.org/10.1080/03081087.2018.1470602
  10. W. Li, W.-H. Liu, S. Vong, On the Z-eigenvalue bounds for a tensor, Numer. Math. Theor. Meth. Appl. Vol. 11, No. 4, pp. 810-826
  11. W. Li, D. Liu, S. Vong, Comparison results for splitting iterations for solving multi-linear systems, Applied Numerical Mathematics, https://doi.org/10.1016/j.apnum.2018.07.009
  12. H. Zheng, S. Vong,  L. Liu, The relaxation modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems. International Journal of Computer Mathematics, https://doi.org/10.1080/00207160.2018.1504928
  13. *H. Zheng, S. Vong, The modulus-based nonsmooth Newton’s method for solving a class of nonlinear complementarity problems of P-matrices. Calcolo, https://doi.org/10.1007/s10092-018-0279-y [Rank=17/313≈5% @Mathematics]
  14. D. Liu, W. Li, M. K. Ng, S. Vong, Uniqueness and perturbation bounds for sparse non-negative tensor equations, Frontiers of Mathematics in China, August 2018, Volume 13, Issue 4, pp 849–874

2019:

  1. **S. Vong, C. Shi^, D. Liu^, Improved exponential stability criteria of time-delay systems via weighted integral inequalities, Applied Mathematics Letters, 86, 14-21 [Rank=9/252≈4% @Mathematics, applied]
  2. *H. Zheng, S. Vong, A modified modulus-based matrix splitting iteration method for solving implicit complementarity problems, Numerical Algorithms, https://doi.org/10.1007/s11075-018-0614-z [Rank=24/254≈9%  @Mathematics, applied]
  3. S Vong, C Shi^, P Lyu^, A study on a second order finite difference scheme for fractional advection–diffusion equations, Numerical Methods for Partial Differential Equations 35 (2) March 2019, 493-508
  4. S. Vong, P. Lyu, On a second order scheme for space fractional diffusion equations with variable coefficients, Applied Numerical Mathematics 137, 34-48
  5. *H Zheng, S Vong, L Liu, A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices, Applied Mathematics and Computation 353, 396-405 .[Rank=14/254≈6% @Mathematics, applied]
  6. **P Lyu, S Vong, A graded scheme with bounded grading for a time-fractional Boussinesq type equation, Applied Mathematics Letters 92, 35-40 [Rank=9/252≈4% @Mathematics, applied]
  7. *H Zheng, S Vong, WX Guo, Newton-type methods for solving quasi-complementarity problems via sign-based equation, Calcolo 56 (2), 20 [Rank=17/313≈5% @Mathematics]
  8. *P. Lyu, S. Vong, A High-Order Method with a Temporal Nonuniform Mesh for a Time-Fractional Benjamin-Bona-Mahony Equation, Journal of Scientific Computing, https://doi.org/10.1007/s10915-019-00991-6 [Rank=26/254≈10%  @Mathematics, applied]
  9. D. Liu, W. Li, S. Vong, Relaxation Methods for Solving the Tensor Equation Arising from the Higher-order Markov Chains, to appear in Numerical Linear Algebra with Applications.
  10. W. Li, W.-H. Liu and S. Vong, Perron vector analysis for irreducible nonnegative tensors and its applications, to appear in J. Ind. Manag. Optim.
  11. X. Ge, X.S. Chen, S. Vong, Inexact generalized Noda iterations for generalized eigenproblems, to appear in Journal of Computational and Applied Mathematics
  12. J. Ren, D. Shi, S. Vong, High accuracy error estimates of a Galerkin FEM for nonlinear time fractional diffusion equation, to appear in Numerical Methods for Partial Differential Equations
  13. P. Lyu, S. Vong, A nonuniform L2 formula of Caputo derivative and its application to a fractional BBM-type equation with nonsmooth solutions, to appear in Numerical Methods for Partial Differential Equations,  https://doi.org/10.1002/num.22441
  14. *C. Shi^, S. Vong, Finite-time stability for discrete-time systems with time-varying delay and nonlinear perturbations by weighted inequalities, Journal of the Franklin Institute, https://doi.org/10.1016/j.jfranklin.2019.09.028 [Rank=7/105≈7% @ Mathematics, interdisciplinary appliactions]
  15. *H. Zheng, S. Vong, On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices, Applied Mathematics and Computation, https://doi.org/10.1016/j.amc.2019.124890. [Rank=14/254≈6% @Mathematics, applied]
  16. **P. Lyu, S. Vong, An efficient numerical method for q-fractional differential equations, to appear in Applied Mathematics Letters [Rank=9/252≈4% @Mathematics, applied]

^This author is a student under my supervision when he completed this article.

Papers indexed by Scopus:

  1. Z. Bai, X. Jin, and S. Vong, On Some Inverse Singular Value Problems with Toeplitz-Related   Structure, Numerical Algebra, Control and Optimization, 2 (2012)  187-192.
  2. W. Qu, S. Lei, S. Vong, A note on the stability of a second order finite difference scheme for space fractional diffusion equations. Numer. Algebra Control Optim.  4  (2014),  no. 4, 317–325.
  3. W. Li, W.H. Liu, S. Vong, On the bound of the eigenvalue in module for a positive tensor, J. Operations Research Society of China, 5 (2017), 123–129.

Book

  1. X. Jin and S. Vong, An Introduction to Applied Matrix Analysis, Higher Education Press, Beijing; and World Scientific, Singapore, 2016, xiii+130 pages. ISBN 978-981-4749-46-6.  [A copy of this Book is exhibited in E1 (University Gallery) of UM]

Edited Book

  1. X. Jin, H. Sun and S. Vong (2011), Recent Advances in Scientific Computing and Matrix Analysis, International Press, Boston, Somerville

Conference Papers and Book Contributions

  1. S. Vong (1998). On the Vacuum State for the Equations of Isentropic Gas Dynamics II, Proceedings of Luso-Chinese Symposium on Nonlinear Evolution Equations and their Applications, Macao.
  2. S. Vong, W. Wang and X. Jin (2006). A Note on the Complexity of the PCG Algorithm for Solving Toeplitz Systems with a Fisher-Hartwig Singularity, Proceedings of Computational Methods in Engineering and Science (EPMESC) X,Hainan,China.
  3. Y. Zhang, S. Vong and X. Jin, A Family of Generating Functions with An Application in Finance, Proceedings of the 4th East AsiaSIAM Conference, Daejeon, Korea, MINS, October 2008, pp. 7-14.
  4. S. Vong, A bound on spectrum of circulant preconditioned elliptic operators, Recent Advances in Computational Mathematics, Higher Education Press, Beijing & International Press of Boston, Somerville, 2008, pp. 163-172.
  5. Z. Li, S. Vong, Y. Wei, and X. Jin, Some Results on Condition Numbers, Handbook of Optimization Theory: Decision Analysis and Applications (Mathematics Research Developments), pp. 577-586. Eds: J. Varela and S. Acuña, Nova Science Pub., 2011.

Master Student

  • Cheang Ka Hang (2010)
  • Fok Hou Kei (2012)
  • Wang Zhi Bo (2013), (FDCT student prize winner)
  • Lyu Pin (2015)
  • Guo Li (2015)
  • Shi Chenyang (2017)
  • Yang Hao (2019)
  • He Jiewen (on going)

PhD Student

  • Wang Zhi Bo (2015)
  • Lyu Pin (2018)
  • Liu Dongdong (2018)
  • Shi Chenyang (on going)
  • Yao Zhongsheng (on going)
  • Ge Xiao (on going)

Contact Details

Faculty of Science and Technology
University of Macau, E11
Avenida da Universidade, Taipa,
Macau, China

Room: E11-3069
Telephone: (853) 8822-4359
Fax: (853) 8822-2426
Email: swvong