ments ▁and ▁furn iture ▁by ▁John ▁Douglas ▁ ▁References ▁ ▁Further ▁reading ▁ ▁Category : Ch urch ▁of ▁England ▁church ▁buildings ▁in ▁Ch esh ire ▁Category : G rade ▁II * ▁listed ▁churches ▁in ▁Ch esh ire ▁Category : English ▁Goth ic ▁architecture ▁in ▁Ch esh ire ▁Category : G oth ic ▁Rev ival ▁architecture ▁in ▁Ch esh ire ▁Category : John ▁Douglas ▁buildings ▁Category : Di oc ese ▁of ▁Ch ester <0x0A> </s> ▁The ▁Kant or ov ich ▁theorem , ▁or ▁Newton – K ant or ov ich ▁theorem , ▁is ▁a ▁mathematical ▁statement ▁on ▁the ▁semi - local ▁convergence ▁of ▁Newton ' s ▁method . ▁It ▁was ▁first ▁stated ▁by ▁Leon id ▁Kant or ov ich ▁in ▁ 1 9 4 8 . ▁It ▁is ▁similar ▁to ▁the ▁form ▁of ▁the ▁Ban ach ▁fixed - point ▁theorem , ▁although ▁it ▁states ▁existence ▁and ▁uniqu eness ▁of ▁a ▁zero ▁rather ▁than ▁a ▁fixed ▁point . ▁ ▁Newton ' s ▁method ▁construct s ▁a ▁sequence ▁of ▁points ▁that ▁under ▁certain ▁conditions ▁will ▁conver ge ▁to ▁a ▁solution ▁ ▁of ▁an ▁equation ▁ ▁or ▁a ▁vector ▁solution ▁of ▁a ▁system ▁of ▁equation ▁. ▁The ▁Kant or ov ich ▁theorem ▁gives ▁conditions ▁on ▁the ▁initial ▁point ▁of ▁this ▁sequence . ▁If ▁those ▁conditions ▁are ▁satisfied ▁then ▁a ▁solution ▁exists ▁close ▁to ▁the ▁initial ▁point ▁and ▁the ▁sequence ▁converges ▁to ▁that ▁point . ▁ ▁Ass um ptions ▁ ▁Let ▁ ▁be ▁an ▁open ▁subset ▁and ▁ ▁a ▁differenti able ▁function ▁with ▁a ▁Jacob ian ▁ ▁that