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Algebra
Question

Write formulas for obtaining successive Newton's ...

Write formulas for obtaining successive Newton's Method \(f ( x , y , z ) = 0 , g ( x , y , z ) = 0 , h ( x , y , z ) = 0\)

Answer

\(\left. \begin{array} { l } { x = x _ { 0 } - \frac { \Delta _ { 1 } } { \Delta } , \quad y = y _ { 0 } - \frac { \Delta _ { 2 } } { \Delta } , \quad z = z _ { 0 } - \frac { \Delta _ { 3 } } { \Delta } } \\ { \text { where } \Delta = \frac { \partial ( f , g , h ) } { \partial ( x , y , z ) } | _ { ( x _ { 0 } , y _ { 0 } , z _ { 0 } ) } } \\ { \text { and } \Delta _ { i } \text { is } \Delta \text { with the } i \text { th column replaced with } \left. \begin{array} { l } { f } \\ { h } \end{array} \right. } \end{array} \right.\)

Solution
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