Related papers: An introduction to the Equiangular algorithm
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
In this paper we present an efficient algorithm to compute the eigen decomposition of a matrix that is a weighted sum of the self outer products of vectors such as a covariance matrix of data. A well known algorithm to compute the eigen…
A new reorthogonalized block classical Gram--Schmidt algorithm is proposed that factorizes a full column rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has orthonormal columns) and $R$ is upper triangular and nonsingular. With…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
We present a Bayesian scheme for the approximate diagonalisation of several square matrices which are not necessarily symmetric. A Gibbs sampler is derived to simulate samples of the common eigenvectors and the eigenvalues for these…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly…
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
We investigate determinantal varieties for symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic variables in quantum field theories. We study the ideals of…