黄娜1, 马昌凤1, 谢亚君2
黄娜, 马昌凤, 谢亚君. 求解非对称代数Riccati 方程几个新的预估-校正法[J]. 计算数学, 2013, 35(4): 401-418.
Huang Na, Ma Changfeng, Xie Yajun. SOME PREDICTOR-CORRECTOR-TYPE ITERATIVE SCHEMES FOR SOLVING NONSYMMETRIC ALGEBRAIC RICCATI EQUATIONS ARISING IN TRANSPORT THEORY[J]. Mathematica Numerica Sinica, 2013, 35(4): 401-418.
Huang Na1, Ma Changfeng1, Xie Yajun2
MR(2010)主题分类:
分享此文:
[1] Juang J, Lin W W. Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices[J]. SIAM J. Matrix Anal. Appl., 1999, 20: 228-243.[2] Juang J. Existence of algebraic matrix Riccati equations arising in transport theory[J]. Linear Algebra Appl., 1995, 230: 89-100.[3] Lu L Z. Solution form and simple iteration of a nonsymmetric algebraic Riccati equation arising in transport theory[J]. SIAM J. Matrix Anal. Appl., 2005, 26: 679-685.[4] Guo C H, Laub A J. On the iterative solution of a class of nonsymmetric algebraic Riccati equations[J]. SIAM J. Matrix Anal. Appl., 2000, 22: 376-391.[5] Bao L, Lin Y, Wei Y. A modified simple iterative method for nonsymmetric algebraic Riccati equations arising in transport theory[J]. Appl. Math. Comput., 2006, 181: 1499-1504.[6] Bai Z Z, Gao Y H, Lu L Z. Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory[J]. SIAM J. Sci. Comput., 2008, 30: 804-818.[7] C.H. Guo, Lin W W. Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory[J]. Linear Algebra Appl., 2010, 432: 283-291.[8] Wu S, Huang C. Two-step relaxation Newton method for nonsymmetric algebraic Riccati equations arising from transport theory[J]. Math. Probl. Eng., 2009, 12: 1-17.[9] Lin Y. A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory[J]. Comput. Math. Appl., 2008, 56: 3046-3051.[10] Lin Y, Bao L, Wu Q. On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations[J]. Comput. Math. Appl., 2011, 62: 4178-4184.[11] Berman A, Plemmons R J. Nonnegative matrices in the mathematical sciences, Academic Press, New York, 1979.[12] Fiedler M, Ptak V. On matrices with non-positive off-diagonal elements and positive principal minors[J]. Czechoslovak Math. J., 1962, 12: 382-400.[13] Bini D A, Meini B and Poloni F. From algebraic Riccati equations to unilateral quadratic matrix equations: old and new algorithms, Proceeding of Numerical Methods for Structured Markov Chains, Dagstuhl Seminar Proceedings, IBFI, Schloss Dagstuhl, Germany 2008.[14] Bini D A, Meini B and Poloni F. Fast solution of a certain Riccati equation through Cauchy-like matrices[J]. Electron. Trans. Numer. Anal., 2009, 33: 84-104.[15] Gao Y H and Bai Z Z. On inexact Newton methods based on doubling iteration scheme for nonsymmetric algebraic Riccati equations[J]. Numer. Linear Algebra Appl., 2011, 18: 325-341.[16] Guo C H. Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for Mmatrices[J]. SIAM J. Matrix Anal. Appl., 2001, 23: 225-242.[17] Guo X X, Lin W W and Xu S F. A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation[J]. Numer. Math., 2006, 103: 393-412.[18] Juang J and Chen I D. Iterative solution for a certain class of algebraic matrix Riccati equations arising in transport theory[J]. Tansport Theory Statist. Phys., 1993, 22: 65-80.[19] Juang J and Lin Z T. Convergence of an iterative technique for algebraic matrix Riccati euqations and applications to transport theory[J]. Tansport Theory Statist. Phys., 1992, 21: 87-100.[20] Bai Z Z, Guo X X and Xu S F. Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations[J]. Numer. Linear Algebra Appl., 2006, 13: 655-674.[21] Benner P, Mena H and Saak J. On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations[J]. Electr. Trans. Num. Anal., 2008, 29: 136-149.[22] Benner P and Saak J. A Galerkin-Newton-ADI method for solving largescale algebraic Riccati equations, Preprint SPP1253-090, DFG Priority Programme Optimization with Partial Differential Equations, (2010) . URL http:././www.am.unierlangen.de./ home./spp1253./wiki./index.php./Preprints[23] Bini D A, Iannazzo B and Poloni F. A fast Newton's method for a nonsymmetric algebraic Riccati equation[J]. SIAM J. Matrix Anal. Appl., 2008, 30: 276-290.[24] Guo C H, Iannazzo B and Meini B. On the doubling algorithm for a (shifted) nonsymmetric algebraic Riccati equations[J]. SIAM J. Matrix Anal. Appl., 2007, 29: 1083-1100.[25] Lu L Z. Newton iterations for a nonsymmetric algebraic Riccati equation[J]. Numer. Linear Algebra Appl., 2005, 12: 191-200.[26] Li J R and White J. Low-rank solution of Lyapunov equations[J]. SIAM J. Matrix Anal. Appl., 2002, 24: 260-280.[27] Martinsson P G, Rokhlin V and Tygert M. A fast algorithm for the inversion of general Toeplitz matrices[J]. Comput. Math. Appl., 2005, 50: 741-752.[28] Penzl T. A cyclic low-rank smith method for large sparse Lyapunov equations[J]. SIAM J. Sci. Comput., 2000, 21: 1401-1418.[29] Wachspress E L. Optimum alternating-direction-implicit iteration parameters for a model problem[J]. J. Soc. Indust. Appl. Math., 1962, 10: 339-350.[30] Wachspress E L. ADI iteration parameters for solving Lyapunov and Sylvester equations, Note of private communication, 2009.[31] Bai Z Z. On Hermitian and skew-Hermitian splitting iteration methods for continuous Sylvester equations[J]. J. Comp. Math., 2011, 29: 185-198.[32] Bai Z Z, Golub G H and Ng M K. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. SIAM J. Matrix Anal. Appl., 2003, 24: 603-626. |
[1] | 杨学敏, 牛晶, 姚春华. 椭圆型界面问题的破裂再生核方法[J]. 计算数学, 2022, 44(2): 217-232. |
[2] | 古振东. 非线性弱奇性Volterra积分方程的谱配置法[J]. 计算数学, 2021, 43(4): 426-443. |
[3] | 甘小艇. 状态转换下欧式Merton跳扩散期权定价的拟合有限体积方法[J]. 计算数学, 2021, 43(3): 337-353. |
[4] | 李旭, 李明翔. 连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速[J]. 计算数学, 2021, 43(3): 354-366. |
[5] | 古振东, 孙丽英. 非线性第二类Volterra积分方程的Chebyshev谱配置法[J]. 计算数学, 2020, 42(4): 445-456. |
[6] | 闫熙, 马昌凤. 求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析[J]. 计算数学, 2019, 41(1): 37-51. |
[7] | 王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90. |
[8] | 陈圣杰, 戴彧虹, 徐凤敏. 稀疏线性规划研究[J]. 计算数学, 2018, 40(4): 339-353. |
[9] | 古振东, 孙丽英. 一类弱奇性Volterra积分微分方程的级数展开数值解法[J]. 计算数学, 2017, 39(4): 351-362. |
[10] | 刘丽华, 马昌凤, 唐嘉. 求解广义鞍点问题的一个新的类SOR算法[J]. 计算数学, 2016, 38(1): 83-95. |
[11] | 陈绍春, 梁冠男, 陈红如. Zienkiewicz元插值的非各向异性估计[J]. 计算数学, 2013, 35(3): 271-274. |
[12] | 任志茹. 三阶线性常微分方程Sinc方程组的结构预处理方法[J]. 计算数学, 2013, 35(3): 305-322. |
[13] | 范斌, 马昌凤, 谢亚君. 求解非线性互补问题的一类光滑Broyden-like方法[J]. 计算数学, 2013, 35(2): 181-194. |
[14] | 张亚东, 石东洋. 各向异性网格下抛物方程一个新的非协调混合元收敛性分析[J]. 计算数学, 2013, 35(2): 171-180. |
[15] | 陈争, 马昌凤. 求解非线性互补问题一个新的 Jacobian 光滑化方法[J]. 计算数学, 2010, 32(4): 361-372. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||