相关论文: Algorithmic work with orthogonal polynomials and s…

We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…

Let $\cp:=(P_1,...,P_s)$ be a given family of $n$-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by $d$ and $h$, respectively. Suppose furthermore that for…

Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial…

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that…

We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…

An algorithm for image processing is proposed. The proposed algorithm, which can be viewed as a quantum-classical hybrid algorithm, can transform a low-resolution bitonal image of a character from the set of alphanumeric characters (A-Z,…

The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schr\"{o}dinger type and an integral operator of…

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification; coalgebraic generality implies in particular that we cover not only classical…

Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical,…

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…

We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…

The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…

We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…

The representation of polynomials by arithmetic circuits evaluating them is an alternative data structure which allowed considerable progress in polynomial equation solving in the last fifteen years. We present a circuit based computation…

In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…

From the algebraic solution of $x^{n}-x+t=0$ for $n=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these…

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by…

This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…