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- Peizhen Zhu, Andrew V. Knyazev
- J. Num. Math.
- 2013

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e.,… (More)

Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of… (More)

- Peizhen Zhu, Andrew V. Knyazeva
- 2012

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced and used via their cosines. The tangents of PABS have attracted relatively less attention, but are important for analysis of convergence of subspace iterations… (More)

- Peizhen Zhu, Andrew V. Knyazev
- SIAM J. Matrix Analysis Applications
- 2017

- Peizhen Zhu, Merico E. Argentati, Andrew V. Knyazev
- SIAM J. Matrix Analysis Applications
- 2013

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If x is an eigenvector of a self-adjoint bounded operator A in a Hilbert space, then the RQ of the vector x, denoted by (x), is an exact eigenvalue of A. In this case, the absolute change of the RQ j(x) (y)j becomes… (More)

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If x is an eigenvector of a self-adjoint bounded operator A in a Hilbert space, then the RQ of the vector x, denoted by (x), is an exact eigenvalue of A. In this case, the absolute change of the RQ j(x) (y)j becomes… (More)

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