Systems of nonlinear algebraic equations with unique solution

作者：Ciurte Anca; Nedevschi Sergiu; Rasa Ioan^*

来源：Numerical Algorithms, 2015, 68(2): 367-376.

DOI：10.1007/s11075-014-9849-5

• Nonlinear algebraic systems
• Existence and uniqueness of the solution
• Newton-type iterations
• Attraction point

We consider nonlinear algebraic systems of the form , where A is a positive matrix and p a non-negative vector. They are involved quite naturally in many applications. For such systems we prove that a positive solution x (au) exists and is unique. Moreover, we prove that x (au) is an attraction point for three Newton-type iterations. A numerical experiment, concerning the computing times for such iterations, is presented. Previously known results, involving existence and uniqueness of solution for particular functions F and matrices A, are extended and generalized.

• 出版日期2015-2