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Newton Raphson Method is one of the most efficient techniques for solving equations numerically. Learn the formula of the Newton Raphson method, along with solved examples here.
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Jun 5, 2024 · Newton Raphson Method or Newton’s Method is an algorithm to approximate the roots of zeros of the real-valued functions, using guess for the first iteration (x 0) and then approximating the next iteration(x 1) which is close to roots, using the following formula.
Learn how to use the Newton-Raphson method to find the roots of a function by using derivatives. See examples with solutions, advantages, disadvantages and practice problems.
The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function \(f(x) = 0\). It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it.
The Newton-Raphson method, or Newton Method, is a powerful technique for solving equations numerically. Like so much of the di erential calculus, it is based on the simple idea of linear approximation. The Newton Method, properly used, usually homes in on a root with devastating e ciency.
Example 1: calculating square roots of positive numbers with Newton’s method. Newton’s method can be used to calculate the square root of a positive real number. Sounds interesting, doesn’t it? But how does this computational algorithm help to compute square roots? Here is how: Let’s say that we are interested in the square root of 2.
The Newton-Raphson method is based on the principle that if the initial guess of the root of \(f(x) = 0\) is at \(x_{i}\), then if one draws the tangent to the curve at \((x_i,f(x_{i})\), the point \(x_{i + 1}\) where the tangent crosses the \(x\)-axis is an improved estimate of the root (Figure 1).
