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Perspectives and Open Problems
Published in Phillip A. Regalia, Adaptive IIR Filtering in Signal Processing and Control, 2018
Extract from this matrix the Schur complement () Ry/u≜Ryy−RuytRuu−1Ruy.
1
Published in Ervin Sejdić, Tiago H. Falk, Signal Processing and Machine Learning for Biomedical Big Data, 2018
Then according to the Schur complement [24], the marginalized precision matrix K˜OO of zO can be written as K˜OO=KOO−KOHKHH−1KHO=KOO−L,
Linear Systems
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
the block form of Gaussian elimination generally proceeds via the Schur complementS=D−CA−1B (of A in M), M∼I⋮0⋯⋮⋯CA−1⋮IA⋮B⋯⋮⋯C⋮D=A⋮B⋯⋮⋯0⋮S
A procedure for the stiffness identification of parallel robots under measurement limitations
Published in Mechanics Based Design of Structures and Machines, 2023
Rasool Bina, Ali Kamali E., Afshin Taghvaeipour, Alexandr Klimchik
Equation (1) can be rewritten in the following matrix format as well, where and, represent the rotational, translational and coupling stiffness block matrices, with the units of N.m, N/m and N, respectively. Also, the vectors and denote the small-amplitude rotational and translational displacements of the EF, respectively, and the vectors and represent the moment and force vectors exerted on the EF, respectively. The important purpose of this study is to provide an algorithm based on which it is possible to identify the stiffness parameters under the restrictive conditions, both on the force applications and the displacement measurements. Hence, the concept of Schur complements will be incorporated. The Schur complement is a key mathematical tool in the field of numerical analysis (F. Zhang 2006), and it appears when the block Gaussian elimination is performed on the coefficient matrix of a set of linear equations.
Nonlinear Elimination Applied to Radiation Diffusion
Published in Nuclear Science and Engineering, 2020
Thomas A. Brunner, Terry S. Haut, Paul F. Nowak
If one of the block matrices, for example, is easy to invert, we can use a Schur complement to reduce the block linear system with two variables into a smaller system with just one unknown, namely,