Combining this approximation with the value of the true root yields: Unless the derivative \(f'(x_o)\) is close to 0. As \(h\) will be small, a linear tangent line is used to approximate the location of the root and can be written as: The true root can thus be expressed as \(r = x_0 + h\), and therefore \(h = r - x_0\), where \(h\) measures how far the guess is from the true value of the root. According to the above discussion, we can conclude that the Newton Raphson method is an application of derivative which is a power technique to converge a function faster unless the derivative of the function becomes zero.The initial guess of the root is typically denoted \(x_0\) with the true root represented by \(r\). But there are some practical considerations of this method such as it fails when the derivative of a function is zero at its initial guess. ![]() It is a powerful technique to find the fastest convergence of a function to its real root. It is also known as an application of derivative because, NR formula uses the tangent line slope. The Newton Raphson Method is a fundamental concept of numerical analysis. It is a point where the change in a function stops to increase or decrease. Usually the derivative becomes zero on a stationary point. If the derivative of a function becomes zero, the NR method is unable to calculate the real root.If the derivative of a function cannot be easily calculated, the convergence of the NR method slows down. The Newton method requires the derivative of a function to be calculated directly.There are a few practical considerations that affect the convergence of the NR method. Generally its convergence is quadratic as the method converges on the root. Practical Considerations of Newton Raphson MethodĪlthough Newton method is one of the most efficient iterative methods that converges faster. It is used to calculate reactive/active power, voltage or current to get a complete understanding of a power flow system.It is used to analyse the flow in watch distribution networks. ![]()
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