A fast numerical algorithm for finding all real solutions to a system of N nonlinear equations in a finite domain

A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica, Matlab, and Python as examples) do not offer a solution, is to find all the real solutions of a system of n nonlinear equations in a certain finite domain of the n -dimensional space of v...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Numerical algorithms Jg. 99; H. 3; S. 1111 - 1125
Hauptverfasser: Chueca-Díez, Fernando, Gañán-Calvo, Alfonso M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2025
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Applications of mathematics
Computer Science
Edge detection
Hyperspaces
Methods
Nonlinear equations
Numeric Computing
Numerical Analysis
Partial differential equations
Theory of Computation
Domain discretization
All-solutions
Nonlinear systems
Algebraic equations
ISSN:1017-1398, 1572-9265
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:A highly recurrent traditional bottleneck in applied mathematics, for which the most popular codes (Mathematica, Matlab, and Python as examples) do not offer a solution, is to find all the real solutions of a system of n nonlinear equations in a certain finite domain of the n -dimensional space of variables. We present two similar algorithms of minimum length and computational weight to solve this problem, in which one resembles a graphical tool of edge detection in an image extended to n dimensions. To do this, we discretize the n -dimensional space sector in which the solutions are sought. Once the discretized hypersurfaces (edges) defined by each nonlinear equation of the n -dimensional system have been identified in a single, simultaneous step, the coincidence of the hypersurfaces in each n -dimensional tile or cell containing at least one solution marks the approximate locations of all the hyperpoints that constitute the solutions. This makes the final Newton-Raphson step rapidly convergent to all the existent solutions in the predefined space sector with the desired degree of accuracy.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01908-7