• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.297-310
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• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.265-277
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• 1997

Let E be a real, non-degenerate, indefinite inner product space with dim $E \geq 3$. It is shown that any bijection of E which preserves the light cones is an affine map.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.4
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• pp.375-385
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• 2020

In this paper, a special indefinite inner product, named hyperbolic scalar product, is used and all acquired results have been raised and proved with the proviso that the space is equipped with this indefinite scalar product. The main objective is to be introduced and applied an indefinite oblique projection method, called Indefinite Lanczos J-biorthogonalizatiom process, which in addition to building a pair of J-biorthogonal bases for two used Krylov subspaces, leads to the introduction of a process for solving large non-J-symmetric linear systems, i.e., Indefinite two-sided Lanczos Algorithm for Linear systems.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.45.2-45
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• 2002

$\textbullet$ Uncertainties are described by sum quadratic constraint(SQC) $\textbullet$ SQC is converted into an indefinite quadratic cost function $\textbullet$ A Kalman filter developed in indefinite inner product space is Krein space Kalman filter $\textbullet$ To minimize the SQC, the Krein space Kalman filter is used $\textbullet$ The proposed robust filter outperforms the standard Kalman filter and existing robust Kalman filter $\textbullet$ The proposed filter has the same recursive, simple structure as the standard Kalman filter $\textbullet$ Easy to design, adequate for on-line implementation

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.104-109
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• 2002

A new robust Kalman filter is designed for the linear discrete-time system with norm-bounded parametric uncertainties. Sum quadratic constraint, which describes the uncertainties of the system, is converted into an indefinite quadratic form to be minimized in indefinite inner product space. This minimization problem is solved by the new robust Kalman filter. Since the new filter is obtained by simply modifying the conventional Kalman filter, robust filtering scheme can be more readily designed using the proposed method in comparison with the existing robust Kalman filters. A numerical example demonstrates the robustness and the improvement of the proposed filter compared with the existing filters.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-706
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• 2020

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A^†_MN exists, where A is an adjointable operator between Hilbert C^⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A^†_MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.6
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• pp.735-746
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• 1999

We design the robust and inherently fault tolerant decetralized$$H^infty$$ filter for the multisensor state estimation problem when there are insufficient priori informations on the statistical properties of external disturbances. For developing the proposed algorithm, an alternative form of suboptimal$$H^infty$$ filter equations are formulated by applying an alternative form of Kalman filter equations to the indefinite inner product space state model of suboptimal$$H^infty$$ filtering problems. The decentralized$$H^infty$$ filter that consists of local and central fusion filters can be designed effciently using the proposed alternative$$H^infty$$ filiter gain equations. The proposed decentralized$$H^infty$$ filter is robust against un-known external disturbances since it bounds the maximum energy gain from the external disturbances to the estimation errors under the prescribed level$$r^2$$ in both local and central fusion filters and is also fault tolerant due to its inherent redundancy. In addition, the central fusion equations between the global and local data can reduce the unnecessary calculation burden effectively. Computer simulations are made to ceritfy the robustness and fault tolerance of the proposed algorithm.