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A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship
ocal polynomial fitting polynomial regression
2007/12/10
Recently, Gijbels and Rousson suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also ...
Characteristic set method for differential-difference polynomial systems
Characteristic set Differential and difference polynomial Regular ascending chain Irreducible ascending chain Zero decomposition algorithm Perfect ideal membership problem
2013/9/9
In this paper, we present a characteristic set method for mixed differential and difference polynomial systems. We introduce the concepts of coherent, regular, proper irreducible, and strongly irreduc...
Characteristic Set Method for Dierential-Dierence Polynomial Systems
Characteristic set dierence and dierential polynomial coherent ascending chain regular ascending chain irreducible ascending chain zero decomposition algorithm
2013/9/9
In this paper, we present a characteristic set method for mixed dierence and dierential polynomial systems. We introduce the concepts of coherent, regular,proper irreducible, and strong irreducible as...
LINEAR COMPLEXITY AND THE MINIMAL POLYNOMIAL OF LINEAR RECURRING SEQUENCES OVER Z/(m)
Linear complexity over Z/(m) uniqueness
2007/8/7
In this note we discuss the annihilating properties of sequences over Z/(m). By considering the linear complexity and the annihilator structure, we derive the uniqueness condition for the minimal poly...
An Interior-point Trust-region Polynomial Algorithm for Convex Programming
interior-point algorithm self-concordant barrier trust-region subproblem
2012/8/1
An interior-point trust-region algorithm is proposed for minimization of a convex quadratic objective function over a general convex set. The algorithm uses a trust-region model to ensure descent on a...
On Cauchy's Bound for Zeros of a Polynomial
Zeros polynomials upper bound moduli refinement
2010/2/26
In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.
A Polynomial Time Algorithm to Find Rational General Solutions of First Order Autonomous ODEs
Rational general solution rst order autonomous ODE rational parameterizations Laurent series Pade approximants polynomial time algorithm
2013/9/9
We give a necessary and su±cient condition for an algebraic ODE to have a rational type general solution. For a ˉrst order autonomous ODE F = 0, we give an exact degree bound for its rational solution...
UNIVARIATE ORE POLYNOMIAL RINGS IN COMPUTER ALGEBRA
UNIVARIATE POLYNOMIAL RINGS COMPUTER ALGEBRA
2013/9/3
We present some algorithms related to rings of Ore polynomials (or, briefly, Ore rings) and describe a computer algebra library for basic operations in an arbitrary Ore ring. The library can be used a...
Integer Sequences associated with Integer Monic Polynomial
Integer Sequences Integer Monic Polynomial
2010/10/29
To every integer monic polynomial of degree m can be associated m integer sequences having interesting properties to the roots of the polynomial. These sequences can be used to find the real roots of...
Roots of any Polynomial with Complex Integer Coefficients using Replacement Sequences, Ruler and Compass
Roots Polynomial Complex Integer Coefficients Replacement Sequences
2010/11/1
The roots of any polynomial of degree m with complex integer coefficients can be computed by manipulation of sequences made from distinct symbols and counting the different symbols in the sequences. T...
Polynomial and rational solutions of holonomic systems
Polynomial rational solutions holonomic systems
2010/10/29
The aim of this paper is to give two new algorithms, which are elimination free, to find polynomial and rational solutions for a given holonomic system associated to a set of linear differential oper...
Polynomial hulls and H-infinity control for a hypoconvex constraint
Polynomial hulls H-infinity control hypoconvex constraint
2010/10/29
We say that a subset of C^n is hypoconvex if its complement is the union of complex hyperplanes. Let D be the closed unit disk in C, T the unit circle. We prove two conjectures of Helton and Marshall...
Symbolic computation of the roots of any polynomial with integer coefficients
Symbolic computation roots polynomial integer coefficients
2010/11/1
The roots of any polynomial of degree m with integer coefficients, can be computed by manipulation of sequences made from 2m distinct symbols and counting the different symbols in the sequences. This ...
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, whe...
Order in Solving Polynomial Equations.