Recovering an Homogeneous Polynomial from Moments of Its Level Set
نویسنده
چکیده
منابع مشابه
On the shape–from–moments problem and recovering edges from noisy Radon data
Abstract. We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from– moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown tha...
متن کاملA new algorithm for computing SAGBI bases up to an arbitrary degree
We present a new algorithm for computing a SAGBI basis up to an arbitrary degree for a subalgebra generated by a set of homogeneous polynomials. Our idea is based on linear algebra methods which cause a low level of complexity and computational cost. We then use it to solve the membership problem in subalgebras.
متن کاملConvex Optimization and Parsimony of Lp-balls Representation
In the family of unit balls with constant volume we look at the ones whose algebraic representation has some extremal property. We consider the family of nonnegative homogeneous polynomials of even degree p whose sublevel set G = {x : g(x) ≤ 1} (a unit ball) has the same fixed volume and want to find in this family the polynomial that minimizes either the parsimony-inducing 1-norm or the 2-norm...
متن کاملRecovering Exact Results from Inexact Numerical Data in Algebraic Geometry
Let {f1, f2, . . . , ft} ⊂ Q[z1, . . . , zN ] be a set of homogeneous polynomials. Let Z denote the complex, projective, algebraic set determined by the homogeneous ideal I = (f1, f2, . . . , ft) ⊂ C[z1, . . . , zN ]. Numerical continuation-based methods can be used to produce arbitrary precision numerical approximations of generic points on each irreducible component of Z. Consider the prime d...
متن کاملOn Moments of a Polytope
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P ⊂ R is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the density function. Using this, we solve the inverse moment problem for the set of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete & Computational Geometry
دوره 50 شماره
صفحات -
تاریخ انتشار 2013