A new geometric method to prove the total positivity of UE spline basis was proposed.UE spline basis is a kind of basis defined over algebraic-trigonometric unified space.UE spline basis shares most properties of the ...A new geometric method to prove the total positivity of UE spline basis was proposed.UE spline basis is a kind of basis defined over algebraic-trigonometric unified space.UE spline basis shares most properties of the usual polynomial B-Splines.Total positivity is an important property for spline basis,it is highly related with shape preserving and variation diminishing properties.Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it.It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively,not only enrich the UE spline basis theory,but also can be treated as supplement to the total positivity in algebraic sense.This approach also can be extended to other analogical bases.展开更多
基金Supported by the National Science Foundation of China (60970079 and 60933008)
文摘A new geometric method to prove the total positivity of UE spline basis was proposed.UE spline basis is a kind of basis defined over algebraic-trigonometric unified space.UE spline basis shares most properties of the usual polynomial B-Splines.Total positivity is an important property for spline basis,it is highly related with shape preserving and variation diminishing properties.Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it.It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively,not only enrich the UE spline basis theory,but also can be treated as supplement to the total positivity in algebraic sense.This approach also can be extended to other analogical bases.
