Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Numerical_Methods_(Chasnov)/02%3A_Root_Finding/2.02%3A_Newton's_MethodWe have f(xn+1)=f(xn)+(xn+1−xn)f′(xn)+…. To determine xn+1, we drop the higher-order terms in the Taylor...We have f(xn+1)=f(xn)+(xn+1−xn)f′(xn)+…. To determine xn+1, we drop the higher-order terms in the Taylor series, and assume f(xn+1)=0. Solving for xn+1, we have xn+1=xn−f(xn)f′(xn) Starting Newton’s Method requires a guess for x0, hopefully close to the root x=r.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/04%3A_Applications_of_the_Derivative/4.01%3A_Newton's_MethodNewton's Methos is a technique to approximate the solution to equations and is built around tangent lines. The main idea is that if x is sufficiently close to a root of f(x), then the tangent line to ...Newton's Methos is a technique to approximate the solution to equations and is built around tangent lines. The main idea is that if x is sufficiently close to a root of f(x), then the tangent line to the graph at (x,f(x) will cross the x-axis at a point closer to the root than x.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/06%3A_Applications_of_the_Derivative/6.03%3A_Newton's_MethodNewton's method is a way to find a solution to the equation to as many decimal places as you want. It is what is called an "iterative procedure,'' meaning that it can be repeated again and again to ge...Newton's method is a way to find a solution to the equation to as many decimal places as you want. It is what is called an "iterative procedure,'' meaning that it can be repeated again and again to get an answer of greater and greater accuracy. Iterative procedures like Newton's method are well suited to programming for a computer. Newton's method uses the fact that the tangent line to a curve is a good approximation to the curve near the point of tangency.
