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期刊論文  

  1. H.-Y. Fan (2025, May). Inheritance properties for projection methods on continuous-time algebraic Riccati equations. Computational and Applied Mathematics, Vol. 44, No. 6, Paper No. 292, 20 pp. (SCI, 54/347, MATHEMATICS, APPLIED/JCR 2025). NSTC 113-2115-M-003-013. 本人為第一作者、通訊作者.
  2. C.-Y. Chiang, H.-Y. Fan (2024, Aug). Four extremal solutions of discrete-time algebraic Riccati equations: existence theorems and computation. Japan Journal of Industrial and Applied Mathematics, Vol. 41, pp. 1593--1627. (SCI, 149/347, MATHEMATICS, APPLIED/JCR 2025). MOST 110-2115-M-003-016. 本人為通訊作者.
  3. C.-Y. Chiang, H.-Y. Fan (2024, Feb). Inheritance properties of the conjugate discrete-time algebraic Riccati equation. Linear Algebra and its Applications, Vol. 683, pp. 71--97. (SCI, 132/499, MATHEMATCS/JCR 2025). MOST 111-2115-M-003-012. 本人為通訊作者.
  4. H.-Y. Fan, C.-Y. Chiang (2023, Jan). On the maximal solution of the conjugate discrete-time algebraic Riccati equation. Applied Mathematics Letters, Vol. 135, Paper No. 108438, 7 pp. (SCI, 33/347, MATHEMATICS, APPLIED/JCR 2025). MOST 110-2115-M-003-016. 本人為第一作者.
  5. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2020, Jun). Krylov subspace methods for discrete-time algebraic Riccati equations. Applied Numerical Mathematics, Vol. 152, pp. 499--510. (SCI, 43/343, MATHEMATICS, APPLIED/JCR 2024). MOST 107-2115-M-003-003.
  6. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2020, Jun). Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations. Journal of Computational and Applied Mathematics, Vol. 371, Paper No. 112685, 13 pp. (SCI, 35/343, MATHEMATICS, APPLIED/JCR 2024). MOST 108-2115-M-003-004.
  7. L. Zhang, E. K.-W. Chu, H.-Y. Fan, Y. Wei (2020, May). Small-sample statistical condition estimation of rational Riccati equations. Applied Mathematics Letters, Vol. 103, Paper No. 106172, 7 pp. (SCI, 28/343, MATHEMATICS, APPLIED/JCR 2024). MOST 108-2115-M-003-004. 本人為通訊作者.
  8. B. Yu, H.-Y. Fan, E. K.-W. Chu (2019, Dec). Large-scale algebraic Riccati equations with high-rank constant terms. Journal of Computational and Applied Mathematics, Vol. 361, pp. 130--143. (SCI, 53/331, MATHEMATICS, APPLIED/JCR 2023). MOST 107-2115-M-003-003. 本人為通訊作者.
  9. B. Yu, H.-Y. Fan, E. K.-W. Chu (2018, Jun). Smith method for projected Lyapunov and Stein equations. University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, Vol. 80, No. 2, pp. 191--204. (SCI, 161/267, MATHEMATICS, APPLIED/JCR 2022).
  10. H.-Y. Fan, L. Zhang, E. K.-W. Chu, Y. Wei (2017, Dec). Numerical solution to a linear equation with tensor product structure. Numerical Linear Algebra With Applications, Vol. 24, No. 6, e2106, pp. 1--18. (SCI, 31/333, MATHEMATICS/JCR 2021). MOST 105-2115-M-003-003. 本人為第一作者.
  11. H.-Y. Fan, E. K.-W. Chu (2017, May). Projected nonsymmetric algebraic Riccati equations and refining estimates of invariant and deflating subspaces. Journal of Computational and Applied Mathematics, Vol. 315, pp. 70--86. (SCI, 37/267, MATHEMATICS, APPLIED/JCR 2021). MOST 105-2115-M-003-003. 本人為第一作者.
  12. H.-Y. Fan, L. Zhang, E. K.-W. Chu, Y. Wei (2016, Feb). Q-less QR decomposition in inner product spaces. Linear Algebra and its Applications, Vol. 491, pp. 291--316. (SCI, 87/330, MATHEMATICS/JCR 2020). MOST 104-2115-M-003-003. 本人為第一作者.
  13. H.-Y. Fan, P. C.-Y. Weng, E. K.-W. Chu (2016, Feb). Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control. Numerical Algorithms, Vol. 71, No. 2, pp. 245--272. (SCI, 24/265, MATHEMATICS, APPLIED/JCR 2020). MOST 102-2115-M-003-009. 本人為第一作者.
  14. L. Zhang, H.-Y. Fan, E. K.-W. Chu, Y. Wei (2015, Feb). Homotopy for rational Riccati equations arising in stochastic optimal control. SIAM Journal on Scientific Computing, Vol. 37, No. 1, pp. B103--B125. (SCI, 31/254, MATHEMATICS, APPLIED/JCR 2018). MOST 102-2115-M-003-009. 本人為通訊作者.
  15. H.-Y. Fan, P. C.-Y. Weng, E. K.-W. Chu (2014, Mar). Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils. BIT, Vol. 54, No. 1, pp. 147--169. (SCI, 82/254, MATHEMATICS, APPLIED/JCR 2018). NSTC 102-2115-M-003-009. 本人為第一作者.
  16. C.-Y. Chiang, H.-Y. Fan, M. M. Lin, H.-A. Chen (2013, Dec). Perturbation analysis of the stochastic algebraic Riccati equation. Journal of Inequalities and Applications, 2013, 2013:580. (SCI, 106/311, MATHEMATICS/JCR 2016). NSTC 102-2115-M-003-009.
  17. C.-Y. Chiang, H.-Y. Fan (2013, Jan). Residual bounds of the stochastic algebraic Riccati equation. Applied Numerical Mathematics, Vol. 63, pp. 78--87. (SCI, 98/255, MATHEMATICS, APPLIED/JCR 2016). 本人為通訊作者.
  18. P. C.-Y. Weng, H.-Y. Fan, E. K.-W. Chu (2012, Oct). Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory. Applied Mathematics and Computation, Vol. 219, No. 2, pp. 729--740 . (SCI, 35/255, MATHEMATICS, APPLIED/JCR 2016). NSTC 100-2115-M-003-004. 本人為通訊作者.
  19. E. K.-W. Chu, H.-Y. Fan, Z. Jia, T. Li, W.-W. Lin (2011, Feb). The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs. Journal of Computational and Applied Mathematics, Vol. 235, No. 8, pp. 2626--2639. (SCI, 55/254, MATHEMATICS, APPLIED/JCR 2015).
  20. C.-Y. Chiang, H.-Y. Fan, W.-W. Lin (2010, Jun). A structured doubling algorithm for discrete-time algebraic Riccati equations with singular control weighting matrices. Taiwanese Journal pf Mathmatics, Vol. 14, No. 3A, pp. 933--954. (SCI, 107/302, MATHEMATICS/JCR 2013). NSTC 97-2115-M-003-010. 本人為通訊作者.
  21. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2007). Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems. SIAM Journal on Matrix Analysis and Applications, Vol. 29, No. 3, pp. 982–1006. (SCI, 38/245, MATHEMATICS, APPLIED/JCR 2011). NSTC 94-2115-M-264-003.
  22. H.-Y. Fan, W.-W. Lin, S.-F. Xu (2005, Oct). Pole assignment in descriptor periodic systems. Science in China Series A-Mathematics, Vol. 48, No. 10, pp. 1309--1332. (SCI). 本人為第一作者.
  23. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2005, Feb). A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations. Linear Algebra and its Applications, Vol. 396, pp. 55--80. (SCI).
  24. H.-Y. Fan, W.-W. Lin, P.Van Dooren (2004, Sep). Normwise scaling of second order polynomial matrices. SIAM Journal on Matrix Analysis and Applications, Vol. 26, No. 1, pp. 252--256. (SCI). 本人為第一作者.
  25. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin, C.-S. Wang (2004, May). Structure-preserving algorithms for periodic discrete-time algebraic Riccati equations. International Journal of Control, Vol. 77, N0. 8, pp. 767--788. (SCI).













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    研討會論文

    1. C.-Y. Chiang, H.-Y. Fan (2025, Jun). Inheritance Properties of Conjugate Discrete-Time Algebraic Riccati Equations. The 26th Conference of the International Linear Algebra Society (ILAS 2025) , National Sun Yat-sen University, Kaohsiung, Taiwan. MOST 111-2115-M-003-012. 本人為通訊作者. Jun 23--27. (Invited Talk).
    2. C.-Y. Chiang, H.-Y. Fan(2024, Jun). An Accelerated Technique for Computing Extremal Solutions ofDiscrete-Time Algebraic Riccati Equations. The 17th SIAM East Asian Section Conference 2024 (EASIAM 2024), University of Macau, Nacao SAR, China. MOST 110-2115-M-003-016. 本人為通訊作者. Jun 28--Jul 1. (Invited Talk).
    3. C.-Y. Chiang, H.-Y. Fan(2023, Aug). An Accelerated Iteration for Finding Extremal Solutions of Discrete-Time Algebraic Riccati Equations. The 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), Waseda University, Tokyo, Japan. MOST 110-2115-M-003-016. 本人為通訊作者. Aug 20--25. (Contribution Talk).
    4. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2019, Jun). The Inheritance ofKrylov Subspace Methods for Large Discrete-Time Algebraic Riccati Equations. The 14th SIAM East Asian Section Conference 2019 (EASIAM 2019), Wuhan University, Wuhan, China. MOST 107-2115-M-003-003. Jun 13--16. (Contribution Talk).
    5. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2018, Jun). Inheritance Properties of the Krylov Subspace Method for Solving Continuous-Time Algebraic Riccati Equations. The 13th SIAM: East Asian Section Conference 2018 (EASIAM 2018), Tokyo, Japan. MOST 106-2115-M-003-002. 本人為通訊作者. Jun 22--25. (Contribution Talk).
    6. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2017, Jun). The Inheritance Properties of Projection Methods for Solving Large-Scale Algebraic Riccati Equations. The 12th SIAM: East Asian Section Conference 2017 (EASIAM 2017), Seoul, South Korea. MOST 105-2115-M-003-003. Jun 22--25. (Contribution Talk).
    7. H.-Y. Fan, L. Zhang, E. K.-W. Chu, Y. Wei (2017, May). Numerical Methods for Solving Linear Systems with Tensor Product Structures. The 5th Taiwan Society for Industrial and Applied Mathematics Annual Meeting, Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan . MOST 105-2115-M-003-003. 本人為第一作者. May 6--7. (Invited Talk).
    8. H.-Y. Fan, L. Zhang, E. K.-W. Chu, Y. Wei (2016, Jun). An Iterative Method for Solving Linear Systems with Tensor Product Structures. The 11th East Asia Section of SIAM Conference (EASIAM 2016), Macau, China. MOST 104-2115-M-003-003. 本人為第一作者. Jun 20--22. (Contribution Talk).
    9. H.-Y. Fan, P. C.-Y. Weng, E. K.-W. Chu (2014, Aug). Iterative Methods for Solving Large-Scale Gerneralized Lyapunov/Stein and Rational Riccati Equations. The 19th International Linear Algebra Society Conference (ILAS2014) , Seoul, Korea. NSC 102-2115-M-003-009. 本人為第一作者. Aug 6--9. (Contribution Talk).
    10. C.-Y. Chiang, H.-Y. Fa (2013, Jun). A Posteriori Error Bounds for the Stochastic Algebraic Riccati Equation. The 2nd Conference on Imdustrial and Applied Mathematics (EASIAM-CIAM 2013), Bandung, Indonesia. 本人為通訊作者. Jun 18--20. (Contibution Talk).
    11. C.-Y. Chiang, H.-Y. Fan (2013, Mar). The Normwise Residual Bounds for the Stochastic Algebraic Riccati Equation. The 1st Cross-straits Optimization Workshop, Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan . 本人為通訊作者. Mar 27--29. (Invited Talk).
    12. P. C.-Y. Weng, H.-Y. Fan, E. K.-W. Chu (2012, Jun). A Large-Scale Nonsymmetric Algebraic Riccati Equation from Transport Theory. 2012 SIAM Conference on Applied Linear Algebra, Valencia, Spain. NSC 100-2115-M-003-004. 本人為通訊作者. Jun 18--22. (Contribution Talk).
    13. H.-Y. Fan (2009, Aug). The Iterative Refinement for Periodic Eigenvalue Problems. The 7th International Conference on Numerical Optimization and Numerical Linear Algebra, Lijiang, Yunnan, China. Aug 16--19. (Contribution Talk).
    14. H.-Y. Fan (2008, Dec). Structure-Preserving Doubling Algorithm for Solving Algebraic Riccati Equations with Singular Control Weighting Matrices. Mathematical Meeting & Annual Meeting of the Mathematical Society, National Tsing Hua University, Hsinchu, Taiwan. Dec 19--21. (Contribution Talk).
    15. H.-Y. Fan (2008, Jan). A Structured Doubling Algorithm for Algebraic Riccati Equations with Singular Control Weighting Matrices. Recent Advances in Numerical Methods for Eigenvalue Problems, National Tsing Hua University, Hsinchu, Taiwan. Jan 4--8. (Contribution Talk).
    16. H.-Y. Fan (2007, Jul). Balanced Realization of Periodic Discrete-Time Descriptor Systems. International Workshop of Linear Algebra in Control, Fudan University, Shanghai, China. Jul 22--24. (Invited Talk).
    17. H.-Y. Fan (2006, Dec). Scaling for Second Order Polynomial Matrices. The 15th Workshop on Differential Equations, Southern Taiwan University of Technology, Tainan, Taiwan. Dec 22--24. (Invited Talk) .
    18. H.-Y. Fan (2004, Sep). Reachability/Observability Gramians and Balanced Realization of Periodic Descriptor Systems. International Conference on Numerical Analysis and Applied Mathematics 2004, Technological Educational Institution of Chalkis, Chalkis, Greece.

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    技術報告  

    1. C.-Y. Chiang, H.-Y. Fan(2022, Dec). Inheritance Properties of the Conjugate Discrete-Time Algebraic Riccati Equation. arXiv:2212.01966. https://arxiv.org/abs/2212.01966. MOST 111-2115-M-003-012.
    2. H.-Y. Fan, C.-Y. Chiang (2022, May). On the Maximal Solution of the Conjugate Discrete-Time Algebraic Riccati Equation. arXiv:2205.14423. https://arxiv.org/abs/2205.14423. MOST 110-2115-M-003-016.
    3. C.-Y. Chiang, H.-Y. Fan (2021, Nov). An Efficient Iteration for the Extremal Solutions of Discrete-Time Algebraic Riccati Equations. arXiv:2111.08923. https://arxiv.org/abs/2111.08923. MOST 110-2115-M-003-016,
    4. L. Zhang, E. K.-W. Chu, H.-Y. Fan, Y. Wei (2019, Sep). Small-Sample Statistical Condition Estimation of Rational Riccati Equations. Preprint 2019-006, NCTS, National Taiwan University, Taipei 106, Taiwan.
    5. L. Zhang, H.-Y. Fan, E. K.-W. Chu (2017, Dec). Inheritance Properties of Projection Methods for Continuous-Time Algebraic Riccati Equations. Preprint 2017-003, NCTS, National Taiwan University, Taipei 106, Taiwan.
    6. H.-Y. Fan, P. C.-Y. Weng, E. K.-W. Chu (2013, Dec). Refining Estimates of Invariant and Deflating Subspaces for Large and Sparse Matrices and Pencils Via Projected Nonsymmetric Algebraic Riccati Equations . Preprint 2013-12-002, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    7. H.-Y. Fan, P. C.-Y. Weng, E. K.-W. Chu (2013, Oct). Refining Estimates of Invariant and Deflating Subspaces for Large and Sparse Matrices and Pencils . Preprint 2013-10-001, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    8. C.-Y. Weng, H.-Y. Fan, E. K.-W. Chu (2012). A Large-Scale Nonsymmetric Algebraic Riccati Equation from Transport Theory. Preprint 2012-2-001, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    9. Matthew M. Lin, C.-Y. Chiang, H.-A. Chen, H.-Y. Fan (2012). Perturbation Analysis of the Stochastic Algebraic Riccati Equation. Preprint 2012-1-003, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    10. C.-Y. Chiang, H.-Y. Fan (2011). Residual Bounds of the Stochastic Algebraic Riccati Equation. Preprint 2011-12-005, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    11. C.-Y. Chiang, H.-Y. Fan, W.-W. Lin (2007). A Structured Doubling Algorithm for Discrete-Time Algebraic Riccati Equations with Singular Control Weighting Matrices. Preprint 2007-5-001, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    12. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2005). Rayleigh-Ritz Approximation and Refinement of Periodic Matrix Pairs. Preprint 2005-1-003, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    13. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2005). Reachability and Observability of Periodic Descriptor Systems. Preprint 2005-1-009, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    14. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2005). Projected Generalized Discrete-Time Periodic Lyapunov Equations and Balanced Realization of Periodic Descriptor Systems. Preprint 2005-1-010, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    15. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2003). A Structure-Preserving Doubling Algorithm for Continuous-Time Algebraic Riccati Equations. Preprint 2002-28, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    16. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin (2003). A Generalized Structure-Preserving Doubling Algorithm for Generalized Discrete Algebraic Riccati Equations. Preprint 2002-29, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
    17. E. K.-W. Chu, H.-Y. Fan, W.-W. Lin, C.-S. Wang (2003). A Structure-Preserving Doubling Algorithm for Periodic Discrete-Time Algebraic Riccati Equations. Preprint 2002-18, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.

     

    其他  

    1. H.-Y. Fan(2004, Jun). Numerical Study of Algebraic RiccatiEquations and Balanced Realization of Periodic Descriptor Systems. Doctoral dissertation, National Tsing Hua University, Taiwan.
    2. H.-Y.Fan (1999, Jun). Synchronization of CoupledLorenz Systems with Various Boundary Conditions. Master thesis, National TsingHua University, Taiwan.

     

     

     

     

     


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