Related papers: Hessenberg decomposition of matrix fields and boun…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
We determine the decomposition matrices of the Brauer algebra over the complex field.
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…
For a finite connected simple graph, the Terwilliger algebra is a matrix algebra generated by the adjacency matrix and idempotents corresponding to the distance partition with respect to a fixed vertex. We will consider algebras defined by…
We develop two fast algorithms for Hessenberg reduction of a structured matrix $A = D + UV^H$ where $D$ is a real or unitary $n \times n$ diagonal matrix and $U, V \in\mathbb{C}^{n \times k}$. The proposed algorithm for the real case…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.
The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for…
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
This note deals with a simultaneous approximation of several matrices by a finite family of diagonalizable matrices satisfying an additional condition for the spectrum of a matrix product. That is the simplicity of all eigenvalues.
In this paper, a new approach is presented to determine common eigenvalues of two matrices. It is based on Gerschgorin theorem and Bisection method. The proposed approach is simple and can be useful in image processing and noise estimation.
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the…