连续同伦方法的点估计判据

Point Estimates on Continuity Homotopy Method

本文证明了，当S·Smale［1］的点估计判据a（z0，f）＝||Df（z0）-1·f（z0）||sup||Df－1（z0）·时，求Banach空间解析映照f零点的连续同伦H（t，z）≡f（z）＋（t－1）f（z0）＝0有定义于［0，1］上的解z（t），且对t∈［0，1］，Hz（t，z（t））－1存在，进而F（Z（1））＝0，可以用连续同伦方法求得f的零点．

This paper discusses continuity method by the work of Smale's point estimates. The results show that the homotopy H(t,z) ≡f(z) + (t-1)f(z0) =0 has solution z(t) defined on [0,1] and Hz(t,z(t) )-1 exists for all t in [0 1 ]if a(z0 , f) <3 - 2. Hence continuity method can solve f(x) = 0 when analytic map f satisfies a(z0, f) <3 - 2