The Interval Method of Bisection for Solving the Nonlinear Equations with Interval-Valued Parameters

The article dwells on the interval extension of the bisection approach for solving nonlinear equations with interval-valued parameters, i.e. the ones that might have values from the specified bounds. It is shown that such a procedure allows to obtain an interval of possible values for equation root that is entirely determined by the equation parameters inaccuracy and does not depend on any other factor. The proposed interval bisection method can be easily implemented. All the differences from the traditional bisection approach for solving equations have a clear meaning. The simple stopping rule is proposed. It is shown that considering the interval nature of equation parameters makes it possible to finish the iterative process of equation solving earlier in full accordance with known information on the equation parameters. The proposed approach keeps the important bisection method property—all the intermediate estimates of the bounds of the root’s possible values interval include the exact boundaries. The article provides an illustrative example of how to use the interval bisection.