# Semenov's Algorithm for Solving Systems of Nonlinear Equations

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An algorithm due to V. Yu. Semenov computes all the roots that lie in some rectangular domain of of a system of equations (not necessarily polynomial) given by a function , provided the system has no repeated roots in the domain.

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Contributed by: Andrzej Kozlowski (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Suppose we have a system of equations in variables:

1. Suppose that for some with , we have . Then the system has no root in the region .

2. Suppose . Then the system has at most one root in the region .

V. Yu. Semenov, "The Method of Determining All Real Nonmultiple Roots of Systems of Nonlinear Equations," *The Journal of Computational Mathematics and Mathematical Physics*, 47(9), 2007 p. 1428.

## Permanent Citation