![]() We will compare all algorithms against the nonlinear function $f(x)=x^3-x^2-x-1$ which has only one root inside a defined range $$ (this criterion is quite important, otherwise it might be hard to tell which solution we got from the algorithm). In the following chapters, we have a closer look at several algorithms used for root approximation of functions. ![]() We start with an easy approach using Bisection, investigating in Newton and Secant method and are concluding with black-box methods of Dekker and Brent. This time I would like to have a closer look at root approximation methods which I regularly use to solve numerous numerical problems. Thus, with the seventh iteration, we note that the final interval, 1.7266, 1.7344, has a width less than 0. Bisection method applied to f ( x ) x2 - 3. Let step 0.01, abs 0.01 and start with the interval 1, 2. ![]() Numerical Methods with C++ Part 3: Root Approximation Algorithms 15 min read. Consider finding the root of f ( x) x2 - 3.
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