Abstract for Math 499 project (Solving Polynomial Equations)
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Bill Finkenkeller – 11/19/03 <br>

It seems a deceptively easy question to ask for solutions to a simple set of polynomial equations, but it is a hard enough question that people have come up with many different ways to solve a set of equations, each with it’s benefits and drawbacks.  Rice even has a course (caam 353) which deals almost entirely with different methods for solving systems of equations.  One way used to solve a system numerically is Newton’s method, similar to Newton’s method one learns in Calculus 1.  Another, more sophisticated method involves finding a Groebner basis and first finding if the solution set is finite.  Then one can use numerical techniques to solve for one variable at a time from a lexicographic Groebner basis.  Which method is easier?  Which is better?  Which solves the problem faster?  Maybe we’ll find out.