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Matrix Decomposition and Applications
, 2022 In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices.
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Jordan Matrix Decomposition [PDF]
Formalized Mathematics, 2008 We follow the rules: i, j, m, n, k denote natural numbers, K denotes a field, and a, λ denote elements of K. Let us consider K, λ, n. The Jordan block of λ and n yields a matrix over K and is defined by the conditions (Def. 1). (Def. 1)(i) len (the Jordan block of λ and n) = n, (ii) width (the Jordan block of λ and n) = n, and (iii) for all i, j such ...
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Journal of Applied Clinical Medical Physics, EarlyView.Abstract Purpose Histotripsy is a focal tumor therapy that utilizes focused ultrasound (US) to mechanically destroy tissue. To overcome visualization limitations of diagnostic US‐guidance, C‐arm cone beam CT (CBCT)‐guided histotripsy is being developed, for which a mobile C‐arm could increase accessibility. CBCT‐guided histotripsy uses a phantom with a
Grace M. Minesinger +5 more
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Sensors, 2016 The detection of a moving target using an IR-UWB Radar involves the core task of separating the waves reflected by the static background and by the moving target.
Donatien Sabushimike +5 more
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Numerical Matrix Decomposition
, 2021 In 1954, Alston S. Householder published \textit{Principles of Numerical Analysis}, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices.
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Singular random matrix decompositions: distributions [PDF]
Journal of Multivariate Analysis, 2005 Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart ...
González Farías, Graciela +1 more
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Singular random matrix decompositions: Jacobians [PDF]
Journal of Multivariate Analysis, 2005 For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y.
González Farías, Graciela +1 more
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International Journal of Adaptive Control and Signal Processing, EarlyView.Summary Data‐driven forecasting of ship motions in waves is investigated through feedforward and recurrent neural networks as well as dynamic mode decomposition. The goal is to predict future ship motion variables based on past data collected on the field, using equation‐free approaches.
Matteo Diez +2 more
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A matrix decomposition and its applications [PDF]
Linear and Multilinear Algebra, 2014 We show the uniqueness and construction (of the Z matrix in Theorem 2.1, to be exact) of a matrix decomposition and give an affirmative answer to a question proposed in [J. Math. Anal. Appl. 407 (2013) 436-442].
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Performance Triggered Adaptive Model Reduction for Soil Moisture Estimation in Precision Irrigation
International Journal of Adaptive Control and Signal Processing, EarlyView.ABSTRACT Accurate soil moisture information is essential for precise irrigation to enhance water use efficiency. Estimating soil moisture based on limited soil moisture sensors is especially critical for obtaining comprehensive soil moisture information when dealing with large‐scale agricultural fields.
Sarupa Debnath +4 more
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