有理Bernstein基和多元有理Blossoms的注记

Notes on the rational Bernstein bases and the multirational Blossoms

利用指数为分数的二项式定理,将Bernstein基推广到分数次,发展了分数次Bernstein基,得到了与整数次Bern-stein基许多类似的性质及恒等式,而这些性质及恒等式对于整数次Bernstein基仍成立,并且给出了关于分数次Bernstein基的Marsden恒等式及Blossoming形式。文中实例表明,负分数次Bernstein基比负整数次Bernstein基具有更大的灵活性。

Fractional Bernstein bases are introduced by observing that the binomial theorem is valid for fractional exponents. Bernstein bases are extended to fractional degree. Many similar properties and identities, which are valid for integral Bernstein bases, are got. Moreover,Marsden identity and its Blossoming form for fractional Bernstein bases are given and the example shows that fractional Bernstein bases are more flexible than integral Bernstein bases.