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Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
Finding roots in a specific region of the complex plane, typically the real roots or the real roots in a given interval (for example, when roots represents a physical quantity, only the real positive ones are interesting). For finding one root, Newton's method and other general iterative methods work generally well.
If x is a simple root of the polynomial , then Laguerre's method converges cubically whenever the initial guess, , is close enough to the root . On the other hand, when x 1 {\displaystyle \ x_{1}\ } is a multiple root convergence is merely linear, with the penalty of calculating values for the polynomial and its first and second derivatives at ...
This consists in using the last computed approximate values of the root for approximating the function by a polynomial of low degree, which takes the same values at these approximate roots. Then the root of the polynomial is computed and used as a new approximate value of the root of the function, and the process is iterated.
Before continuing to the roots of (), it might be necessary to numerically improve the accuracy of the root approximations for (), for instance by Newton's method. Graeffe's method works best for polynomials with simple real roots, though it can be adapted for polynomials with complex roots and coefficients, and roots with higher multiplicity.
A few steps of the bisection method applied over the starting range [a 1;b 1].The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
Given a continuous function defined from [,] to such that () (), where at the cost of one query one can access the values of () on any given .And, given a pre-specified target precision >, a root-finding algorithm is designed to solve the following problem with the least amount of queries as possible:
The red curve shows the function f, and the blue lines are the secants. For this particular case, the secant method will not converge to the visible root. In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f.