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This paper investigates a specific class of perturbed Toeplitz-plus-Hankel matrices. We introduce two novel algorithms designed for perturbed symmetrical centrosymmetrical Toeplitz-plus-Hankel systems, offering reduced computational time. ...

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient algorithm for ...

A randomized algorithm for computing a data sparse representation of a given rank-structured matrix A (a.k.a. an H-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the assumption ...

In this paper the total positivity of the Gramian (mass) matrices of q-Bernstein bases is analyzed. Furthermore, we provide an efficient method to obtain a bidiagonal decomposition of these mass matrices allowing us to calculate their singular ...

In this paper, we consider how to accurately solve the singular value problem and the linear system for a class of Polynomial-Vandermonde-type (PVT) matrices, which belongs to the class of negative matrices introduced by Huang and Xue (Adv Comput ...

We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume ...

Krylov subspace methods for solving linear systems of equations involving skew-symmetric matrices have gained recent attention. Numerical equivalences among Krylov subspace methods for nonsingular skew-symmetric linear systems have been given in ...${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}}$${}^{\mathrm{}}$

By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of their rows ...

Many numerical problems with input $x$ and output $y$ can be formulated as a system of equations $F(x,y)=0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this numerical problem, one ...

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is ...

A correction, along with an improvement, is made on a recent joint work of the second author and the third author. An optimal perturbation bound is also clarified for certain 2 × 2 Hermitian matrices.

In the present paper, we consider the solution of periodic tridiagonal Toeplitz linear systems. By exploiting the special low-rank and Toeplitz structure, we give a new structure-preserving decomposition form of the coefficient matrix. Based on ...$\mathit{}$

The subject of this study is the analysis of the spectral secant equation for the well-known Davidon–Fletcher–Powell (DFP) quasi-Newton updating formula. More precisely, we plan to make the memoryless DFP formula well conditioned in several ...

Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms need $(2q+2)...$

Co-clustering algorithms can seek homogeneous sub-matrices into a dyadic data matrix, such as a document-word matrix. Algorithms for co-clustering can be expressed as a non-negative matrix tri-factorization problem such that X ≈ FSG ⊤, which is ...

• Our algorithm works by multiplicative update rules and it is convergence.
• Adding two penalties for controlling the orthogonality of row and column clusters.
• Unifying a class of algorithms for co-clustering based on α-divergence.

• All learning models require setting some hyperparameters.
• Hyperparameters impact the algorithm’s performance and affect knowledge extraction.
• Gradient-based and bi-level methods are used to tune hyperparameters.
• The penalty ...

Learning approaches rely on hyperparameters that impact the algorithm’s performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning algorithm. ...

A randomized quaternion singular value decomposition algorithm based on block Krylov iteration (RQSVD-BKI) is presented to solve the low-rank quaternion matrix approximation problem. The upper bounds of deterministic approximation error and ...

The main contribution of this paper is to develop explicit expressions for the Drazin inverse of two kinds of anti-triangular block complex matrices under new assumptions. Further, we apply our results to obtain new formulae for the ...

We develop structure-preserving incomplete LU type factorizations for preconditioning centrosymmetric matrices and use them to numerically solve centrosymmetric and nearly centrosymmetric linear systems arising from spectral methods for partial ...

In this paper, we prove that a $3\rho$-locally maximum volume submatrix $\widehat{A}\in {\mathbb{R}}^{r\times r}$ in the matrix $A\in {\mathbb{R}}^{M\times N}$ can be found in $O\left(M,N,r,\left(log,r,+,{log}_{\rho },r\right)\right)$ operations, and a $\rho$-locally maximum volume submatrix for $\rho ⩽3$ can be found in $O\left(M,N,r^3,{log}_{\rho },r\right)$ operations. Based on these ...