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

作者：Wang, Xiang^*; Tang, Xiao-Bin; Mao, Liang-Zhi

来源：Computers & Mathematics with Applications, 2017, 73(2): 327-338.

DOI：10.1016/j.camwa.2016.11.027

• Second-order Arnoldi method (SOAR)
• Krylov subspace
• Quadratic eigenvalue problems (QEP)
• Arnoldi procedure
• Rayleigh-Ritz orthogonal projection

Based on a pair of square matrices A and B and a vector u, a modified second-order Krylov subspace R-n(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 R-n(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.

• 出版日期2017-1-15
• 单位南昌大学; 对外经济贸易大学