A Note on a Uniqueness Theorem for the Second-Derivative Test of Qi
暂无分享,去创建一个
Qi has given a theorem which guarantees the existence and uniqueness of a zero x* of a function f : Rn → Rn in a bounded closed rectangular convex set [x] ⊂ Rn under more general sufficient conditions than those described by Moore and has defined an operator (the so-called second-derivative operator) together with a test, involving the second-derivative operator, for the existence but not the uniqueness of a zero x* of f in [x].The purpose of the present note is to correct the proof of a theorem of Wolfe containing sufficients conditions for the uniqueness if x* using the second-derivative operator.
[1] Ramon E. Moore. A Test for Existence of Solutions to Nonlinear Systems , 1977 .
[2] L. Qi. A Note on the Moore Test for Nonlinear Systems , 1982 .
[3] A. Neumaier. Interval methods for systems of equations , 1990 .
[4] Michael A. Wolfe. On a Second Derivative Test due to Qi , 1998, Reliab. Comput..