Solving finite algebraic systems using numeric Gröbner bases and eigenvalues
نویسندگان
چکیده
Systems of algebraic equations with finitely many solutions arise in many areas of applied mathematics. Among these are motion planning, robotics, computer−aided design, and graphics. We will discuss the design and implementation of a hybrid symbolic− numeric method, and a Mathematica implementation thereof, that finds all solutions to an algebraic system. It makes use of numeric Gröbner bases and arbitrary−precision numeric eigenvalue computation. We explain in outline how this works, and give a few examples that demonstrate how this can be useful technology independent of Newton’s method local solvers.
منابع مشابه
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