▁the ▁convergence ▁to ▁the ▁solution ▁of ▁ ▁is ▁domin ated ▁by ▁the ▁convergence ▁of ▁the ▁Newton ▁iteration ▁of ▁the ▁quadratic ▁polynomial ▁ ▁towards ▁its ▁smallest ▁root ▁, ▁if ▁, ▁then ▁ ▁The ▁quadratic ▁convergence ▁is ▁obtained ▁from ▁the ▁error ▁estimate ▁ ▁Cor ollary ▁In ▁ 1 9 8 6 , ▁Yam am oto ▁proved ▁that ▁the ▁error ▁evalu ations ▁of ▁the ▁Newton ▁method ▁such ▁as ▁D oring ▁( 1 9 6 9 ), ▁Ost row ski ▁( 1 9 7 1 , ▁ 1 9 7 3 ), ▁G rag g - T ap ia ▁( 1 9 7 4 ), ▁Pot ra - P t ak ▁( 1 9 8 0 ), ▁M iel ▁( 1 9 8 1 ), ▁Pot ra ▁( 1 9 8 4 ), ▁can ▁be ▁derived ▁from ▁the ▁Kant or ov ich ▁theorem . ▁ ▁General izations ▁There ▁is ▁a ▁q - anal og ▁for ▁the ▁Kant or ov ich ▁theorem . ▁For ▁other ▁general izations / vari ations , ▁see ▁Or te ga ▁& ▁Rhein bold t ▁( 1 9 7 0 ). ▁ ▁App lications ▁O ishi ▁and ▁Tan abe ▁claimed ▁that ▁the ▁Kant or ov ich ▁theorem ▁can ▁be ▁applied ▁to ▁obtain ▁reliable ▁solutions ▁of ▁linear ▁programming . ▁ ▁References ▁ ▁Further ▁reading ▁▁ ▁John ▁H . ▁Hub b ard ▁and ▁Barbara ▁Bur ke ▁Hub b ard : ▁Vector ▁Calcul us , ▁Linear ▁Al gebra , ▁and ▁D iffer ential ▁Form s : ▁A ▁Un ified ▁Appro ach , ▁Matrix ▁Ed itions , ▁