一种新的Uzawa-MHSS迭代法求解一类复奇异鞍点问题
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摘要
利用经典的Uzawa法和修正的Hermitian和Skew-Hermitian分裂(MHSS)迭代法,提出一种新的Uzawa-MHSS迭代法求解一类复奇异鞍点问题,得到了该方法的半收敛定理,并分析了其半收敛性.数值实验表明,新迭代方法比经典的Uzawa法和MHSS法在求解鞍点问题时更有效.
Using the classical Uzawa method and modified Hermitian and Skew-Hermitian splitting(MHSS)iterative method,we proposed a new Uzawa-MHSS iterative method for solving a class of complex singular saddle-point problems. We obtained the semi-convergence theroem of the new method,and analyzed its semi-convergence.Numerical experiments show that the new iterative method is more effective than the classical Uzawa method and MHSS method to solve the saddle-point problems.
Using the classical Uzawa method and modified Hermitian and Skew-Hermitian splitting(MHSS)iterative method,we proposed a new Uzawa-MHSS iterative method for solving a class of complex singular saddle-point problems. We obtained the semi-convergence theroem of the new method,and analyzed its semi-convergence.Numerical experiments show that the new iterative method is more effective than the classical Uzawa method and MHSS method to solve the saddle-point problems.
引文
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[10]CHAO Zhen,ZHANG Naimin.A Generalized Preconditioned HSS Method for Singular Saddle Point Problems[J].Numer Algor,2014,66(2):203-221.
[11]JIANG Meiqun,CAO Yang.On Local Hermitian and Skew-Hermitian Splitting Iteration Methods for Generalized Saddle Point Problems[J].J Comput Appl Math,2009,231(2):973-982.
[12]LI Jianlei,ZHANG Qingnian,WU Shiliang.Semi-convergence of the Local Hermitian and Skew-Hermitian Splitting Iteration Methods for Singular Generalized Saddle Point Problems[J].Appl Math E-Notes,2011,11:82-90.
[13]ZHANG Naimin,WEI Yimin.On the Convergence of General Stationary Iterative Methods for Range-Hermitian Singular Linear Systems[J].Numer Lin Alg Appl,2010,17(1):139-154.
[14]Berman A,Plemmons R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1994.
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[17]BAI Zhongzhi,Parlett B N,WANG Zengqi.On Generalized Successive Overrelaxation Methods for Augmented Linear Systems[J].Numerische Mathematik,2005,102(1):1-38.
[2]BAI Zhongzhi,Golub G H,Ng M K.Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems[J].Numer Lin Alg Appl,2007,24(3):603-626.
[3]BAI Zhongzhi,Benzi M,CHEN Fang.Modified HSS Iteration Methods a Class of Complex Symmetric Linear Systems[J].Computing,2010,87(3):93-111.
[4]GUO Xiaoxia,WANG Sheng.Modified HSS Iteration Methods for a Class of Non-Hermitian Positive-Definite Linear Systems[J].Appl Math Comput,2012,218(20):10122-10128.
[5]WU Shiliang,LI Cuixia.On Semi-convergence of Modified HSS Method for a Class of Complex Singular Linear Systems[J].Appl Math Lett,2014,38:57-60.
[6]CHAO Zhen,CHEN Guoliang.A Generalied Modified HSS Method for Sigular Complex Symmetric Linear Systems[J].Numer Algor,2016,73(1):77-89.
[7]BAI Zhongzhi,Golub G H,PAN Jianyu.Preconditioned Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Semedefinite Linear Systems[J].Numer Math,2004,98(1):1-32.
[8]BAI Zhongzhi,Golub G H.Accelerated Hermitian and Skew-Hermitian Splitting Iteration Methods for SaddlePoint Problems[J].IMA J Numer Ana1,2007,27(1):1-23.
[9]BAI Zhongzhi,Golub G H,Ng M K.On Successive-Overrelaxation Acceleration of the Hermitian and SkewHermitian Splitting Iterations[J].Numer Lin Alg Appl,2007,14(4):319-335.
[10]CHAO Zhen,ZHANG Naimin.A Generalized Preconditioned HSS Method for Singular Saddle Point Problems[J].Numer Algor,2014,66(2):203-221.
[11]JIANG Meiqun,CAO Yang.On Local Hermitian and Skew-Hermitian Splitting Iteration Methods for Generalized Saddle Point Problems[J].J Comput Appl Math,2009,231(2):973-982.
[12]LI Jianlei,ZHANG Qingnian,WU Shiliang.Semi-convergence of the Local Hermitian and Skew-Hermitian Splitting Iteration Methods for Singular Generalized Saddle Point Problems[J].Appl Math E-Notes,2011,11:82-90.
[13]ZHANG Naimin,WEI Yimin.On the Convergence of General Stationary Iterative Methods for Range-Hermitian Singular Linear Systems[J].Numer Lin Alg Appl,2010,17(1):139-154.
[14]Berman A,Plemmons R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1994.
[15]SONG Yongzhong.Semiconvergence of Block SOR Method for Singular Linear Systems with p-Cyclic Matrices[J].J Comp Appl Math,2001,130(1/2):217-229.
[16]Miller J J H.On the Location of Zeros of Certain Classes of Polynomials with Applications to Numerical Analysis[J].J Inst Math Appl,1971,8(3):397-406.
[17]BAI Zhongzhi,Parlett B N,WANG Zengqi.On Generalized Successive Overrelaxation Methods for Augmented Linear Systems[J].Numerische Mathematik,2005,102(1):1-38.