Finding all solutions of nonlinear equations using the dual simplex method

Interval Methods for Non‐Linear Equation Solving Applications

“…This is commonly used in nonlinear equation solving methods prior to use of the contraction methods discussed below. A method that makes more extensive use of function range testing was developed by Yamamura [91], based on use of linear combinations of the component functions of f (x). An approach for forming the linear combinations based on the inverse of the midpoint of the interval extension of the Jacobian of f (x) was shown to be very effective.…”

“…Implementation of interval methods for nonlinear equation solving typically employ a combination of one or more of the concepts outlined above [10,16,41], perhaps also in connection with some manipulation of the equation system to be solved [46,47,91]. Often function range testing and constraint propagation techniques are used first to contract intervals, as these methods have low computational overhead.…”

A New Approach To Find All Solutions Of Fuzzy Nonlinear Equations

“…In [1] and [2] an approach has proposed to find all solutions of system of nonlinear equations in crisp environment by using a test to determine the existence and nonexistence of solutions in a box. Unfortunately, in some situations because of lack of knowledge, the parameters of the problem can't be modeled in the crisp manner.…”

An interval algorithm for finding all solutions of non‐linear resistive circuits

“…As a computational method to ÿnd all solutions of non-linear equations, interval analysis based techniques are well-known, and various algorithms based on interval computation have been developed [3][4][5]8]. Using the interval algorithms, all solutions of non-linear equations contained in a given box ‡ can be found with mathematical certainty [8].…”

“…However, the computation time of the interval algorithms tends to grow exponentially with the number of variables n. Therefore, in order to apply the interval algorithms to practical circuits, it is necessary to improve the computational e ciency from various viewpoints. Recently, all solutions of systems of 200 non-linear equations could be obtained in practical computation time [5].…”