A modified second-order Arnoldi method for solving the quadratic eigenvalue problems

详细信息    查看全文

• 作者：Xiang Wang^a ; ^b ; ^{wangxiang49@ncu.edu.cn} ; Xiao-Bin Tang^c ; Liang-Zhi Mao^a ; ^b
• 关键词：Second-order Arnoldi method (SOAR) ; Krylov subspace ; Quadratic eigenvalue problems (QEP) ; Arnoldi procedure ; Rayleigh&ndash ; Ritz orthogonal projection
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：327-338
• 全文大小：541 K
• 卷排序：73

文摘

Based on a pair of square matrices AA and BB and a vector uu, a modified second-order Krylov subspace Rn(A,B;u)Rn(A,B;u) is first defined, which generalizes the standard Krylov subspace and the second-order Krylov subspace proposed by Bai and Su (2005). Then a modified second-order Arnoldi procedure for generating an orthonormal basis of Rn(A,B;u)Rn(A,B;u) has been presented. By applying the standard Rayleigh–Ritz orthogonal projection technique, a modified second-order Arnoldi method (MSOAR) for solving a large-scale quadratic eigenvalue problems (QEP) has been proposed. Finally, numerical experiments are given to show the efficiency of the new method.