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A note on the structured perturbation analysis for the inversion formula of Toeplitz matrices
The invertibility of a Toeplitz matrix can be assessed based on the solvability of two standard equations. The inverse of the nonsingular Toeplitz...
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Universal eigenvalue statistics for dynamically defined matrices
We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE...
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Positive Semi-Definite Matrices
The present chapter deals essentially with positive semi-definite matrices. It is the longest chapter of the book, but the reader should be aware...
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Stable Recovery and the Coordinate Small-Ball Behaviour of Random Vectors
Recovery procedures in Data Science are often based on stable point separation. In its simplest form, stable point separation implies that if f is...
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Tensor completion via multi-directional partial tensor nuclear norm with total variation regularization
This paper addresses the tensor completion problem, whose task is to estimate missing values with limited information. However, the crux of this...
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Improved bounds for the RIP of Subsampled Circulant Matrices
In this paper, we study the restricted isometry property of partial random circulant matrices. For a bounded subgaussian generator with independent...
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Numerical Study of a Fast Two-Level Strang Splitting Method for Spatial Fractional Allen–Cahn Equations
In this paper, a numerical method to solve the multi-dimensional spatial fractional Allen–Cahn equations has been investigated. After...
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A finite elements approach for spread contract valuation via associated two-dimensional PIDE
We study an efficient approach based on finite elements to value spread options on commodities whose underlying assets follow a dynamic described by...
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Do the Mittag–Leffler Functions Preserve the Properties of Their Matrix Arguments?
The matrix Mittag–Leffler (ML) functions are receiving great attention at the moment. As a matter of fact, in many applications, the matrix argument...
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Maximizing products of linear forms, and the permanent of positive semidefinite matrices
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this...
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Embedding of Markov matrices for \(\varvec{d \leqslant 4}\)
The embedding problem of Markov matrices in Markov semigroups is a classic problem that regained a lot of impetus and activities through recent needs...
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Self-Dual Hadamard Bent Sequences
A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application (Solé, et al., 2021). The...
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On eigenvalues of a high-dimensional Kendall’s rank correlation matrix with dependence
In this paper, we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix. The underlying population...
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Low-Rank Tensor Data Reconstruction and Denoising via ADMM: Algorithm and Convergence Analysis
Seismic data is contaminated by noise due to a variety of factors including wind, ocean currents, vehicular traffic, and construction. Further...
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Geometric Oversight
In this chapter we give an overview of the main geometric players related to a projective hypersurface, among them the polar map and image, the...
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Proximal linearization methods for Schatten p-quasi-norm minimization
Schatten p -quasi-norm minimization has advantages over nuclear norm minimization in recovering low-rank matrices. However, Schatten p -quasi-norm...
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Enhanced Low-Rank Tensor Recovery Fusing Reweighted Tensor Correlated Total Variation Regularization for Image Denoising
Most current methods for image denoising exploit the global low-rankness and local smoothness priors of images to model them, including independent...
