Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivari...Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.展开更多
In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. ...In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.展开更多
基金Supported by the National Natural Science Foundation of China （Grant Nos. 10271022 and 60373093）.
文摘Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.
基金supported by a GRF grant from the Research Grants Council of the Hong Kong SAR(No.CityU 11310716)
文摘In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.
