![]() Instead of manually computing the first derivative, we will let Python to symbolically differentiate the function. We will use Python symbolic toolbox to perform differentiation. We will use Python to code the Newton method. Or by recalling that the zeros of the quadratic function directly participate in the coefficients: This can be seen by either recalling the formula for the zeros of the quadratic equation The zeros of this function are obviously at x=-3 and x=-7. Let us write the Python code to compute this solution. Pick an initial guess of the solution for, that is, select.So Newton’s method can be summarized as follows From the above figure, we see that the slope of the function at the point is given byįrom the last equation, we can determine as follows Let us formulate this procedure mathematically. By repeating this procedure iteratively, we define a series of points that under some conditions that we will not discuss here, will converge to the solution of ( 1). That is, we generate the tangent line at the point. Then, we repeat this procedure for the point. This function will intersect the x axis at the point. The basic idea is to compute a line that passes through the point and and that is tangent to the function. The idea of Newton’s method is shown is illustrated in the Figure below. Starting from some initial guess of the variable that is denoted by. The purpose of Netwon’s method is to solve the equations having the following form: First, we briefly revise Newton’s method.
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