A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis
نویسندگان
چکیده
We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.
منابع مشابه
A 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 کاملA regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method
The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...
متن کاملSmoothed analysis of condition numbers and complexity implications for linear programming
We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance to ill-posedness of a linear program subject to a slight Gaussian perturbation. In particular, we show that for every n-by-d matrix Ā, n-vector b̄, and d-vector c̄ satisfying ∥∥Ā, b̄, c̄∥∥ F ≤ 1 and every σ ≤ 1, E A,b,c [logC(A, b, c)] = O(log(nd/σ)), where A, b and c ar...
متن کاملar X iv : g r - qc / 0 30 30 40 v 2 1 A pr 2 00 3 Detecting ill posed boundary conditions in General Relativity
A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein equations and analyze its well posedness using the LaplaceFourier technique. By using this technique ill posed modes can be detected and thus a necessary condit...
متن کاملPresenting a Modified SPH Algorithm for Numerical Studies of Fluid-Structure Interaction Problems
A modified Smoothed Particle Hydrodynamics (SPH) method is proposed for fluid-structure interaction (FSI) problems especially, in cases which FSI is combined with solid-rigid contacts. In current work, the modification of the utilized SPH concerns on removing the artificial viscosities and the artificial stresses (which such terms are commonly used to eliminate the effects of tensile and numeri...
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:
- CoRR
دوره abs/0909.4101 شماره
صفحات -
تاریخ انتشار 2009