Related papers: Kunchenko's Polynomials for Template Matching
We present new polynomial-based methods for discrete-time quaternionic systems, highlighting how noncommutative multiplication modifies classical control approaches. Defining quaternionic polynomials via a backward-shift operator, we…
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the…
Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…
Let $\Phi_n(q)$ be the $n$-th cyclotomic polynomial in $q$. Recently, the author and Zudilin provide a creative microscoping method to prove some $q$-supercongruences mainly modulo $\Phi_n(q)^3$ by introducing an additional parameter $a$.…
Using purely combinatorial means we obtain results on simultaneous Diophantine approximation modulo 1 for systems of polynomials with real coefficients and no constant term.
Classical orthogonal polynomials have widespread applications including in numerical integration, solving differential equations, and interpolation. Changing basis between classical orthogonal polynomials can affect the convergence,…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
We develop a marking system for an analog of Hasse diagrams of intervals $[u,v]$ with $u\leq v$ in a Hermitian symmetric pair $W/W_J$, and use this to create a closed form algorithm for computing relative R-polynomials. The uniform nature…
We consider the problem of matching a template to a noisy signal. Motivated by some recent proposals in the signal processing literature, we suggest a rank-based method and study its asymptotic properties using some well-established…
The invited review of own algorithms and software (MAVKA and MCV) for the data analysis of astronomical signals - irregularly spaced, multi-periodic multi-harmonic, periodogram analysis and approximations with taking into account a…
In this paper we consider images of (ordinary) noncommutative polynomials on matrix algebras endowed with a graded structure. We give necessary and sufficient conditions to verify that some multilinear polynomial is a central polynomial, or…
The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…
Krawtchouk polynomials appear in a variety of contexts, most notably as orthogonal polynomials and in coding theory via the Krawtchouk transform. We present an operator calculus formulation of the Krawtchouk transform that is suitable for…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…
We obtain several Cauchy-like and Pellet-like results for the zeros of a general complex polynomial by considering similarity transformations of the squared companion matrix and the reformulation of the zeros of a scalar polynomial as the…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interval containing the support of the target spectral density,…