Optimization Strategies for the Floating-point Gcd
نویسندگان
چکیده
We describe algorithms for computing the greatest common divisor (GCD) of two univariate polynomials with inexactly-known coeecients. Assuming that an estimate for the GCD degree is available (e.g., using an SVD-based algorithm), we formulate and solve a nonlinear optimization problem in order to determine the coeecients of the \best" GCD. We discuss various issues related to the implementation of the algorithms and present some preliminary test results.
منابع مشابه
Approximate 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 کاملThe Numerical Greatest Common Divisor of Univariate Polynomials
This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in conventional GCD computation is identified by its geometry where polynomials form differentiable manifolds entangled in a stratification structure. With a proper r...
متن کاملChapter 1 Regularization and Matrix Computation in Numerical Polynomial Algebra
Numerical polynomial algebra emerges as a growing field of study in recent years with a broad spectrum of applications and many robust algorithms. Among the challenges in solving polynomial algebra problems with floating-point arithmetic, difficulties frequently arise in regularizing ill-posedness and handling large matrices. We elaborate regularization principles for reformulating the illposed...
متن کاملDevelopment of a Novel Floating In-situ Gelling System for Stomach Specific Drug Delivery of the Narrow Absorption Window Drug Baclofen
The present study deals with development of a floating in-situ gel of the narrow absorption window drug baclofen. Sodium alginate-based in-situ gelling systems were prepared by dissolving various concentrations of sodium alginate in deionized water, to which varying concentrations of drug and calcium bicarbonate were added. Fourier transform infrared spectroscopy (FTIR) and differential scannin...
متن کاملDevelopment of a Novel Floating In-situ Gelling System for Stomach Specific Drug Delivery of the Narrow Absorption Window Drug Baclofen
The present study deals with development of a floating in-situ gel of the narrow absorption window drug baclofen. Sodium alginate-based in-situ gelling systems were prepared by dissolving various concentrations of sodium alginate in deionized water, to which varying concentrations of drug and calcium bicarbonate were added. Fourier transform infrared spectroscopy (FTIR) and differential scannin...
متن کامل