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Systems of nonlinear algebraic equations with unique solution

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Abstract

We consider nonlinear algebraic systems of the form \(F(x)= Ax+p, x\in \mathbb {R}^{n}_{+}\), 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 ∗ exists and is unique. Moreover, we prove that x ∗ 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.

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Authors and Affiliations

  1. Technical University of Cluj Napoca, Department of Computer Science, 26-28th G. Baritiu Street, 400027, Cluj-Napoca, Romania

    Anca Ciurte & Sergiu Nedevschi

  2. Technical University of Cluj Napoca, Department of Mathematics, 26-28th G. Baritiu Street, 400027, Cluj-Napoca, Romania

    Ioan Rasa

Authors
  1. Anca Ciurte
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  2. Sergiu Nedevschi
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  3. Ioan Rasa
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Correspondence to Ioan Rasa.

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Ciurte, A., Nedevschi, S. & Rasa, I. Systems of nonlinear algebraic equations with unique solution. Numer Algor 68, 367–376 (2015). https://doi.org/10.1007/s11075-014-9849-5

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  • DOI: https://doi.org/10.1007/s11075-014-9849-5

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