8/5/2023 0 Comments Find root mathematica![]() ![]() Xnew = xtable - (f(xtable)/fp.subs(x,xtable)) The following is a screenshot of the input and output of the built-in function evaluating the roots based on three initial guesses.Īlternatively, a Mathematica code can be written to implement the Newton-Raphson method with the following output for three different initial guesses:ĭef f(x): return sp.sin(5*x) + sp.cos(2*x) The function “FindRoot” applies the Newton-Raphson method with the initial guess being “x0”. Mathematica has a built-in algorithm for the Newton-Raphson method. Setting the maximum number of iterations, ,, the following is the Microsoft Excel table produced: ExampleĪs an example, let’s consider the function. Second, the inverse can be slow to calculate when dealing with multi-variable equations. The first is that this procedure doesn’t work if the function is not differentiable. ![]() This makes the procedure very fast, however, it has two disadvantages. Note: unlike the previous methods, the Newton-Raphson method relies on calculating the first derivative of the function. Setting an initial guess, tolerance, and maximum number of iterations :Īt iteration, calculate and. Where is the estimate of the root after iteration and is the estimate at iteration. To find the root of the equation, the Newton-Raphson method depends on the Taylor Series Expansion of the function around the estimate to find a better estimate : In addition, it can be extended quite easily to multi-variable equations. The reason for its success is that it converges very fast in most cases. The Newton-Raphson method is one of the most used methods of all root-finding methods. Derivatives Using Interpolation Functions.High-Accuracy Numerical Differentiation Formulas.Basic Numerical Differentiation Formulas.Linearization of Nonlinear Relationships.Convergence of Jacobi and Gauss-Seidel Methods.Cholesky Factorization for Positive Definite Symmetric Matrices. ![]()
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