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Newton's Method

# Newton's Method - MA 132 Sequences Newtons Method Julia...

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MA 132 Julia Bielaski-0163140 Sequences: Newton’s Method 11/21/08 1. The Newton Method or the Newton-Raphson Method is a numerical root finder. The method is used when to find the root, r, using a graph or a polynomial expression. The first approximation made is labeled x 1 and it is found by either an educated guess or from a sketch of the graph of a function, f. Basically, the point of the method is that the tangent line is close the f equation and therefore the x-intercept of the tangent line is close to the x-intercept of f. A simple equation is used to calculate this approximation; x n+1 =x n – [f(x n )/f 1 (x n )]. If the x n numbers continue to grow closer to the value of r and the value of n increases then the sequence of x n converges to r. However, the Newton method may not always be the best method to use. For instance, if the approximation does not fit within the domain of f then another method needs to be used. When using the Newton Method, the idea is to get the approximation as accurate as possible. The general rule is that the value of x n and x n+1 should agree to eight decimal places. Lastly, this is known as an iterative process, which basically means that it is predominantly agreeable for use with a graphing calculator or a computer. 2.

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Newton's Method - MA 132 Sequences Newtons Method Julia...

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