Related papers: On Computing the Kronecker Structure of Polynomial…
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…
We study the dynamics of polynomials with coefficients in a non-Archimedean field $K,$ where $K$ is a field containing a dense subset of algebraic elements over a discrete valued field $k.$ We prove that every wandering Fatou component is…
We show that if a polynomial filled Julia set has empty interior, then it is computable.
The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
In this paper we introduce the concept of matrix-valued $q$-rational functions. In comparison to the classic case we give different characterizations with principal emphasise on realizations and discuss algebraic manipulations. We also…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional…
We establish a new class of integrable {\it systems of Kowalevski type}, associated with discriminantly separable polynomials of degree two in each of three variables. Defining property of such polynomials, that all discriminants as…
In this paper we derive new sufficient conditions for a linear system matrix $$S(\lambda):=\left[\begin{array}{ccc} T(\lambda) & -U(\lambda) \\ V(\lambda) & W(\lambda) \end{array}\right],$$ where $T(\lambda)$ is assumed regular, to be…
We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
In this paper, we study a structured family of matrices whose entries are given by products of $k$-Fibonacci and $k$-Lucas numbers. For this family, we obtain explicit and unified formulas for several classical matrix invariants, including…
In this paper, we introduce a new family of equations for matrix pencils that may be utilized for the construction of strong linearizations for any square or rectangluar matrix polynomial. We provide a comprehensive characterization of the…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
Kronecker products of unitary Fourier matrices play important role in solving multilevel circulant systems by a multidimensional Fast Fourier Transform. They are also special cases of complex Hadamard (Zeilinger) matrices arising in many…
We relate the $m$-truncated Kronecker products of symmetric functions to the semi-invariant rings of a family of quiver representations. We find cluster algebra structures for these semi-invariant rings when $m=2$. Each {\sf g}-vector cone…