Numerically determining solutions of systems of polynomial equations
نویسندگان
چکیده
منابع مشابه
Numerically Determining Solutions of Systems of Polynomial Equations
In this report we suggest some efficient algorithms for numerically determining all solutions of a system of n polynomial equations in n unknowns. Such systems are common in many fields of engineering. When all equations are linear, there is at most one isolated solution. In the general case, even the number of solutions can be difficult to predict. By a classical theorem of Bézout, the number ...
متن کاملCoupled systems of equations with entire and polynomial functions
We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1} A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We derive a priory estimates for the sums of the rootsof the considered system andfor the counting function of roots.
متن کاملPolynomial solutions of differential equations
A new approach for investigating polynomial solutions of differential equations is proposed. It is based on elementary linear algebra. Any differential operator of the form L(y) = k=N ∑ k=0 ak(x)y, where ak is a polynomial of degree ≤ k, over an infinite ground field F has all eigenvalues in F in the space of polynomials of degree at most n, for all n. If these eigenvalues are distinct, then th...
متن کاملNumerically Solving Polynomial Systems with Bertini
Numerically Solving Polynomial Systems with Bertini • approaches numerical algebraic geometry from a user's point of view with many worked examples, • teaches how to use Bertini and includes a complete reference guide, • treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic ...
متن کاملSmall solutions to systems of polynomial equations with integer coefficients
The paper discusses a series of conjectures due to A. Tyszka aiming to describe boxes in which there exists at least one solution to a system of polynomial equations with integer coefficients. A proof of the bound valid in the linear case is given. 1 Two basic questions When facing systems of equations whose solutions are hard to determine, one is satisfied to determine (or at least estimate) t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1988
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1988-15639-x