# Some computational methods for systems of nonlinear equations and systems of polynomial equations

@article{Frster1992SomeCM, title={Some computational methods for systems of nonlinear equations and systems of polynomial equations}, author={W. Főrster}, journal={Journal of Global Optimization}, year={1992}, volume={2}, pages={317-356} }

This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed…

## 6 Citations

Parallel schemes of computation for Bernstein coefficients and their application

- MathematicsProceedings. International Conference on Parallel Computing in Electrical Engineering
- 2002

An approach to the range evaluation of a function over an interval is established and coefficients of Bernstein polynomials are effectively calculated in some parallel process for obtaining all solutions of nonlinear equations.

A Geometrical Root Finding Method for Polynomials, with Complexity Analysis

- Mathematics
- 2013

The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to…

Interval Methods for Analog Circuits

- Computer Science
- 2013

In this chapter a version of the predictor-corrector method for computing points of continua‐ tion path of a nonlinear equation is presented and Krawczyk operator is used in ndimensional box-searching of all solutions.

Chapter 4 Interval Methods for Analog Circuits

- Computer Science
- 2013

In this chapter a version of the predictor-corrector method for computing points of continua‐ tion path of a nonlinear equation is presented and Krawczyk operator is used in ndimensional box-searching of all solutions.

Solving Polynomial Systems by Penetrating Gradient Algorithm Applying Deepest Descent Strategy

- Computer ScienceArXiv
- 2015

The most prominent feature of penetrating gradient algorithm is its ability to see and penetrate through the obstacles in error space along the line of search direction and to jump to the global minimizer in a single step.

Quantifier Elimination and Cylindrical Algebraic Decomposition

- MathematicsTexts and Monographs in Symbolic Computation
- 1998

1 Introduction to the Method.- 2 Importance of QE and CAD Algorithms.- 3 Alternative Approaches.- 4 Practical Issues.- Acknowledgments.- Quantifier Elimination by Cylindrical Algebraic Decomposition…

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