Existence and uniqueness of solutions to a nonlinear algebraic equation

Existence and uniqueness of soiutions to a nonlinear aigebraic equation 

A single linear algebraic equation, ax = b, is easily solved, and the condition for existence and uniqueness of the solution x = b/a, a 0, is trivial. For a single nonlinear algebraic equation 

Typically, we are presented with a nonlinear function that is not simple to factorize, and so we know nothing about the number of real solutions. The methods described in this chapter are designed to search for a real solution starting from an initial guess and will be demonstrated on systems with varying numbers of solutions. 

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