Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #39 · Multivariable Calculus · Partial derivatives

In Newton’s method the new guess comes from … by an iteration…

In Newton’s method the new guess comes from $(x_{n}, y_{n})$ by an iteration: $x_{n + 1} = G (x_{n}, y_{n})$ and $y_{n + 1} = H (x_{n}, y_{n})$ . What are $G$ and $H$ for $g = x^{2} - y = 0, h = x - y = 0$ ? First find $Δ x$ and $Δ y$ ; then $x_{n} + Δ x$ gives $G$ and $y_{n} + Δ y$ gives $H$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #39

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