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The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…
Certified model reduction for high-dimensional nonlinear control systems remains challenging: unlike balanced truncation for LTI systems, most nonlinear reduction methods either lack computable worst-case error bounds or rely on intractable…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…
Understanding how bound states in the continuum (BICs) emerge in periodic metasurfaces is essential for the controlled design of high-Q resonances and their systematic manipulation. Here, we investigate the singular value decomposition…
In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…
The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications…
A parallel, blocked, one-sided Hari--Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair $(F,G)$ is here proposed, where $F$ and $G$ have the same number of columns, and are both…
The Singular Value Decomposition (SVD) of matrices is a widely used tool in scientific computing. In many applications of machine learning, data analysis, signal and image processing, the large datasets are structured into tensors, for…
To realize mmWave massive MIMO systems in practice, Beamspace MIMO with beam selection provides an attractive solution at a considerably reduced number of radio frequency (RF) chains. We propose low-complexity beam selection algorithms…
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…
A Cross-Product Free (CPF) Jacobi-Davidson (JD) type method is proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair $(A,B)$. It implicitly solves the mathematically equivalent…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order…
The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem…
Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…
Cross-correlation function (CCF) has become the standard tool for extraction of radial-velocity and broadening information from high resolution spectra. It permits integration of information which is common to many spectral lines into one…
Learning to restore multiple image degradations within a single model is quite beneficial for real-world applications. Nevertheless, existing works typically concentrate on regarding each degradation independently, while their relationship…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
Cross-spectral image guided denoising has shown its great potential in recovering clean images with rich details, such as using the near-infrared image to guide the denoising process of the visible one. To obtain such image pairs, a…