Results 101 to 110 of about 28,414 (283)
On Moore-Penrose inverses of Toeplitz matrices
Linear Algebra and its Applications, 1992 AbstractThe Moore-Penrose inverses of Toeplitz matrices can always be represented as a sum of products of lower and upper triangular Toeplitz matrices, which extends the well-known theorem by Gohberg and Semencul regarding the inverses of Toeplitz matrices.
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A novel constraint‐tightening approach for robust data‐driven predictive control
International Journal of Robust and Nonlinear Control, Volume 35, Issue 7, Page 2566-2587, 10 May 2025.Abstract In this paper, we present a data‐driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time‐invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured
Christian Klöppelt +3 more
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Minimal properties of Moore-Penrose inverses
Linear Algebra and its Applications, 1994 AbstractLet Ax = y be consistent; let x0 = Gy be any minimum-norm solution satisfying (AG)′ = AG; and let A+ be the Moore-Penrose inverse of A. It is shown that φ(G) ⩾ φ(A+) for any φ in a class Φ containing the unitarily invariant matrix norms. The conditioning of the system Ax = y is studied via condition numbers Cφ(A, G). It is shown that Cφ(A, G) ⩾
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Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations
Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 995-1041, May 2025.Abstract The randomly pivoted Cholesky algorithm (RPCholesky) computes a factorized rank‐k$k$ approximation of an N×N$N \times N$ positive‐semidefinite (psd) matrix. RPCholesky requires only (k+1)N$(k + 1)N$ entry evaluations and O(k2N)$\mathcal {O}(k^2 N)$ additional arithmetic operations, and it can be implemented with just a few lines of code.
Yifan Chen +3 more
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About the group inverse and Moore-Penrose inverse of a product
Linear Algebra and its Applications, 1991 AbstractLet A be a matrix over a ring. Suppose that P, Q, P′, and Q′ are matrices over the ring such that P′PA=A=AQQ′. If A has group inverse A#, then PAQ has a group inverse iff AA#QPA+1−AA#is invertible. An analogous result for Moore-Penrose inverses is also given.
M.C. Gouveia, R. Puystjens
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Affine Generalized Inverse for Optimal Control Allocation [PDF]
This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced.
Acheson, Michael J.
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Characterization and Representation of Weighted Core Inverse of Matrices
, 2020 In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are explored.
Behera, Ratikanta +2 more
core
Notes on the Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized projectors [PDF]
The University Thought: Publication in Natural Sciences, 2017 The aim of this paper is to give alternate representations of the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors and to provide alternate proofs of the invertibility of some linear combination of commuting ...
Tošić Marina
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Singular matrices possessing the triangle property
Special MatricesIt is known that the inverse of an invertible real square matrix satisfying the triangle property is a tridiagonal matrix. In this note, results that may be considered as analogues of this assertion are obtained for the Moore-Penrose inverse and the ...
Priya K. Kranthi, Sivakumar K. C.
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Efficient GMM estimation with singular system of moment conditions
Statistical Theory and Related Fields, 2020 Standard generalised method of moments (GMM) estimation was developed for nonsingular system of moment conditions. However, many important economic models are characterised by singular system of moment conditions.
Zhiguo Xiao
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