Tropical Algebraic Geometry in Maple a preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients
نویسندگان
چکیده
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.
منابع مشابه
Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view of this problem leads to efficient preprocessing techniques, applying polyhedral methods on the exact exponents with numerical techniques on the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.
متن کاملApproximate GCD of Multivariate Polynomials
Given two polynomials F and G in R[x1, . . . , xn], we are going to find the nontrivial approximate GCD C and polynomials F , G ∈ R[x1, . . . , xn] such that ||F − CF ′|| < and ||G − CG′|| < , for some and some well defined norm. Many papers 1,2,3,5,8,10,11,13,15 have already discussed the problem in the case n = 1. Few of them 2,10,11 mentioned the case n > 1. Approximate GCD computation of un...
متن کاملAn Algorithm for Approximate Factorization of Bivariate Polynomials
In this paper, we propose a new numerical method for factoring approximate bivariate polynomials over C. The method relies on Ruppert matrix and singular value decomposition. We also design a new reliable way to compute the approximate GCD of bivariate polynomials with floating-point coefficients. The algorithm has been implemented in Maple 9. The experiments show that the algorithms are very e...
متن کاملA Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases
In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...
متن کاملA numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
In this paper, two inverse problems of determining an unknown source term in a parabolic equation are considered. First, the unknown source term is estimated in the form of a combination of Chebyshev functions. Then, a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem. For solving the problem, the operational matrices of int...
متن کامل