Numerically Computing Real Points on Algebraic Sets

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Numerically computing real points on algebraic sets

Given a polynomial system f , a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at...

متن کامل

A Local Dimension Test for Numerically Approximated Points on Algebraic Sets

Given a numerical approximation to a point p on the set V of common zeroes of a set of multivariate polynomials with complex coefficients, this article presents an efficient method to compute the maximum dimension of the irreducible components of V which pass through p, i.e., a local dimension test. Such a test, used to filter out the so-called “junk points,” is a crucial element in the numeric...

متن کامل

Numerically intersecting algebraic varieties via witness sets

The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numeri...

متن کامل

Computing Integral Points in Convex Semi-algebraic Sets

Let Y be a convex set in IR k deened by polynomial inequalities and equations of degree at most d 2 with integer coeecients of binary length l. We show that if Y \ ZZ k 6 = ;, then Y contains an integral point of binary length ld O(k 4). For xed k, our bound implies a polynomial-time algorithm for computing an integral point y 2 Y. In particular, we extend Lenstra's theorem on the polynomial-ti...

متن کامل

Computing real inflection points of cubic algebraic curves

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Acta Applicandae Mathematicae

سال: 2012

ISSN: 0167-8019,1572-9036

DOI: 10.1007/s10440-012-9782-3