Bivariate ideal projectors and their perturbations
نویسنده
چکیده
In this paper we present a complete description of ideal projectors from the space of bivariate polynomials F[x, y] onto its subspace F<n[x, y] of polynomials of degree less than n. Several applications are given. In particular, we study small perturbations of ideal projectors as well as the limits of Lagrange projectors. The latter results verify one particular case of a conjecture of Carl de Boor.
منابع مشابه
On the pointwise limits of bivariate Lagrange projectors
A linear algebra proof is given of the fact that the nullspace of a finite-rank linear projector, on polynomials in two complex variables, is an ideal if and only if the projector is the bounded pointwise limit of Lagrange projectors, i.e., projectors whose nullspace is a radical ideal, i.e., the set of all polynomials that vanish on a certain given finite set. A characterization of such projec...
متن کاملTransfinite mean value interpolation in 3D
s for MAIA 2007 The limits of bivariate Lagrange projectors Carl de Boor∗ and Boris Shekhtman Eastsound, Washington In a talk in Norway in 2003, the first author conjectured that any finite-rank ideal projector (i.e., finite-rank linear projector on the space of polynomials in d variables whose kernel is a polynomial ideal, i.e., a linear space also closed under pointwise multiplication by poly...
متن کاملOn the Limits of Lagrange Projectors
This article addresses a question of Carl de Boor (cf. [3]): What ideal projectors are the limits of Lagrange projectors? The results of this paper answer the question in the sense that for every ideal projector P we prescribe nitely many computations that determine whether the projector P is a limit of Lagrange projectors.
متن کاملSurfaces Generated by Moving Least Squares Methods
An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analys...
متن کاملIdeal Interpolation: Mourrain’s Condition Vs D-invariance
Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain’s characterization requires the polynomial space to be ‘connected to 1’, a condition that is implied by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Adv. Comput. Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2008