Related papers: The antitriangular factorization of skew-symmetric…

First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…

We prove that every holomorphic symplectic matrix can be factorized as a product of holomorphic unitriangular matrices with respect to the symplectic form $ \left[\begin{array}{ccc} 0 & L_n \\ -L_n & 0\end{array}\right]$ where $L$ is the $n…

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

In this paper, we give a description of the skew-symmetrizable matrices and their mutation classes which are determined by the generalized Cartan matrices of affine type.

This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…

Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…

Obtaining the inverse of a large symmetric positive definite matrix $\mathcal{A}\in\mathbb{R}^{p\times p}$ is a continual challenge across many mathematical disciplines. The computational complexity associated with direct methods can be…

We describe the recursive algorithmic procedure to compute the stabilizers of the group of complex orthogonal matrices with respect to the action of similarity on the set of all symmetric matrices. Futhermore, lower bounds for dimensions of…

Sparse matrices, as prevalent primitive of various scientific computing algorithms, persist as a bottleneck in processing. A skew-symmetric matrix flips signs of symmetric pairs in a symmetric matrix. Our work, Parallel 3-Way Banded…

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic…

The partly symmetric real Ginibre ensemble consists of matrices formed as linear combinations of real symmetric and real anti-symmetric Gaussian random matrices. Such matrices typically have both real and complex eigenvalues. For a fixed…

In this article we introduce $K$-type block matrices which include two new classes of block matrices namely block triangular $K$-matrices and hidden block triangular $K$-matrices. We show that the solution of linear complementarity problem…

Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. These point processes are characterised by a matrix valued kernel of skew-orthogonal polynomials. We develop their…

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $BCB^T$, where $C$ is a $k \times k$ symmetric matrix, and both $B$ and $C$ are…

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that…

We equip the complex polynomial algebra C[t] with the involution which is the identity on C and sends t to -t. Answering a question raised by V.G. Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to…

We provide a method to construct $t$-designs from weighing matrices and association schemes. One instance of our method can produce a $3$-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to…

This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…