On the intrinsic complexity of point finding in real singular hypersurfaces

نویسندگان

  • Bernd Bank
  • Marc Giusti
  • Joos Heintz
  • Luis M. Pardo
چکیده

In previous work we designed an efficient procedure that finds an algebraic sample point for each connected component of a smooth real complete intersection variety. This procedure exploits geometric properties of generic polar varieties and its complexity is intrinsic with respect to the problem. In the present paper we introduce a natural construction that allows to tackle the case of a non–smooth real hypersurface by means of a reduction to a smooth complete intersection. MSC:14Q10, 14P05, 14B05, 68W30

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces

For a real squarefree multivariate polynomial F , we treat the general problem of finding real solutions of the equation F = 0 , provided that the real solution set {F = 0}R is compact. We admit that the equation F = 0 may have singular real solutions. We are going to decide whether this equation has a non-singular real solution and, if this is the case, we exibit one for each generically smoot...

متن کامل

Finding sampling points on real hypersurfaces is easier in singular situations

Let f be a polynomial in Q[X1, . . . , Xn] of degree D and, for t ∈ Q, let Ht ⊂ C n be the hypersurface defined by f − t = 0. The main result of this paper is an algorithm computing at least one point in each connected component of H0 ∩ R n, without smoothness assumptions on H0, whose complexity is polynomial in n, the evaluation complexity L of f , D and an intrinsic geometric degree δ which i...

متن کامل

Change Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering

In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change...

متن کامل

Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members

Graphs have so many applications in real world problems. When we deal with huge volume of data, analyzing data is difficult or sometimes impossible. In big data problems, clustering data is a useful tool for data analysis. Singular value decomposition(SVD) is one of the best algorithms for clustering graph but we do not have any choice to select the number of clusters and the number of members ...

متن کامل

Putting into practice deformation techniques for the computation of sampling points in real singular hypersurfaces

Let f be a polynomial in Q[X1, . . . , Xn] of degree D and, for t ∈ Q, Ht ⊂ Cn the hypersurface defined by f − t = 0. We provide a probabilistic algorithm computing at least one point in each connected component of H0 ∩ Rn, without any smoothness assumption on H0 whose worst-case complexity is within O(n2(L + n3)(U(D.δ)2) arithmetic operations in Q (where U(p) denotes the cost of multiplying tw...

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

عنوان ژورنال:
  • Inf. Process. Lett.

دوره 109  شماره 

صفحات  -

تاریخ انتشار 2009