A bisection method for systems of nonlinear equations
ACM Transactions on Mathematical Software (TOMS)
A rapid generalized method of bisection for solving systems of non-linear equations
Numerische Mathematik
Some tests of generalized bisection
ACM Transactions on Mathematical Software (TOMS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Algorithm 554: BRENTM, A Fortran Subroutine for the Numerical Solution of Nonlinear Equations [C5]
ACM Transactions on Mathematical Software (TOMS)
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
An algorithm for the numerical calculation of the degree of a mapping.
An algorithm for the numerical calculation of the degree of a mapping.
Computing the degree of maps and a generalized method of bisection.
Computing the degree of maps and a generalized method of bisection.
ACM Transactions on Mathematical Software (TOMS)
Artificial nonmonotonic neural networks
Artificial Intelligence
FRACTOP: A Geometric Partitioning Metaheuristic for Global Optimization
Journal of Global Optimization
From linear to nonlinear iterative methods
Applied Numerical Mathematics
Sign-based learning schemes for pattern classification
Pattern Recognition Letters - Special issue: Artificial neural networks in pattern recognition
Improved sign-based learning algorithm derived by the composite nonlinear Jacobi process
Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
Novel orbit based symmetric cryptosystems
Mathematical and Computer Modelling: An International Journal
Lipschitz condition for finding real roots of a vector function
Journal of Computational Methods in Sciences and Engineering
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Two algorithms are described here for the numerical solution of a system of nonlinear equations F(X) = &THgr;, Q=0,0,&ldots;,0∈ R , and F is a given continuous mapping of a region D in Rn into Rn . The first algorithm locates at least one root of the sy stem within n-dimensional polyhedron, using the non zero value of the topological degree of F at &thgr; relative to the polyhedron; the second algorithm applies a new generalized bisection method in order to compute an approximate solution to the system. Teh size of the original n-dimensional polyhedron is arbitrary, and the method is globally convergent in a residual sense. These algorithms, in the various function evaluations, only make use of the algebraic sign of F and do not require computations of the topological degree. Moreover, they can be applied to nondifferentiable continuous functions F and do not involve derivatives of F or approximations of such derivatives.