Related papers: A regularization algorithm for matrices of bilinea…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
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…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices and both area-preserving diffeomorphisms and local rotations of the orthonormal frame are realized as…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
A new algorithm for the efficient numerical approximation of weakly singular integrals over convex polytopes is introduced. Such integrals appear in the Galerkin discretizations of integral equations and nonlocal partial differential…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
We study the partial Hadamard matrices $H\in M_{M\times N}(\mathbb C)$ which are regular, in the sense that the scalar products between pairs of distinct rows decompose as sums of cycles (rotated sums of roots of unity). The simplest…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…
In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large…
We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.
Let $\mathcal{G}=[A & M N & B]$ be a generalized matrix algebra defined by the Morita context $(A, B,_AM_B,_BN_A, \Phi_{MN}, \Psi_{NM})$. In this article we mainly study the question of whether there exist proper Jordan derivations for the…
We consider the regularization of matrices $M^N$ written in Jordan form by additive Gaussian noise $N^{-\gamma}G^N$, where $G^N$ is a matrix of i.i.d. standard Gaussians and $\gamma>1/2$ so that the operator norm of the additive noise tends…