A HAMILTONIAN QR ALGORITHM

作     者：BYERS, R 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1986年第7卷第1期

页      面：212-229页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：QR algorithm Hamiltonian matrices symplectic matrices algebraic Riccati equation optimal control 

摘      要：This paper presents a variant $QR$ algorithm for calculating a Hamiltonian–Schur decomposition [10]. It is defined for Hamiltonian matrices that arise from single input control systems. Numerical stability and Hamiltonian structure are preserved by using unitary symplectic similarity transformations. Following a finite step reduction to a Hessenberg-like condensed form, a sequence of similarity transformations yields a permuted triangular matrix. As the iteration converges, it deflates into problems of lower dimension. Convergence is accelerated by varying a scalar shift. When the Hamiltonian matrix is real, complex arithmetic can be avoided by using an implicit double shift technique. The Hamiltonian-Schur decomposition yields the same invariant subspace information as a Schur decomposition but requires significantly less work and storage for problems of size greater than about 20.