Numerical Algorithms

, Volume 6, Issue 2, pp 317–351

# Construction of iteration functions for the simultaneous computation of the solutions of equations and algebraic systems

• Anne-Mercedes Bellido
Article

## Abstract

We construct iteration functions for the simultaneous computation of the solutions of a system of equations, with local quadratic convergence: they generalize to the multivariate case the well-known Weierstrass function for polynomials, which is expected to be globally convergent except on a zero-measured set of starting points. We clarify these functions using univariate interpolation. Both for polynomials and algebraic systems with real coefficients, we extend the conjecture of global convergence to the research of real roots or solutions.

### Keywords

Simultaneous resolution algebraic systems Newton method interpolation

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