We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requi...We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.展开更多
This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are ...This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.展开更多
In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） al...In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.展开更多
基金Supported partly by NSF of China(Grant No.11801163)NSF of Hunan Province(Grant Nos.2021JJ50032,2023JJ50164 and 2023JJ50165)Degree&Postgraduate Reform Project of Hunan University of Technology and Hunan Province(Grant Nos.JGYB23009 and 2024JGYB210).
文摘We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.
文摘This paper proposes the Rice condition numbers for invariant subspace, singular subspaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.
基金supported by the National Natural Science Foundation of China(6167145361201379)Anhui Natural Science Foundation of China(1608085MF123)
文摘In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.
