Numerical analysis of parametrized nonlinear equations
Numerical analysis of parametrized nonlinear equations
A rapid generalized method of bisection for solving systems of non-linear equations
Numerische Mathematik
Finding all isolated solutions to polynomial systems using HOMPACK
ACM Transactions on Mathematical Software (TOMS)
A computational method for finding all the roots of a vector function
Applied Mathematics and Computation
On using estimates of Lipschitz constants in global optimization
Journal of Optimization Theory and Applications
Solving systems of nonlinear equations using the nonzero value of the topological degree
ACM Transactions on Mathematical Software (TOMS)
Note on the end game in homotopy zero curve tracking
ACM Transactions on Mathematical Software (TOMS)
Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Systems
SIAM Journal on Scientific Computing
Subdivision Direction Selection in Interval Methods for Global Optimization
SIAM Journal on Numerical Analysis
Applied Mathematics and Computation
Evaluating Lipschitz Constants for Functions Given by Algorithms
Computational Optimization and Applications
On the complexity of exclusion algorithms for optimization
Journal of Complexity
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Introduction to Numerical Continuation Methods
Introduction to Numerical Continuation Methods
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A new exclusion test for finding the global minimum
Journal of Computational and Applied Mathematics
Optimal algorithms for global optimization in case of unknown Lipschitz constant
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
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Computing real roots of a continuous function is an old and extensively researched problem in numerical computation. Exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain. These algorithms are based on a root condition that can be applied to each cell in the domain. In the present paper, we consider Lipschitz functions of order α and give the root condition for the exclusion algorithms. Furthermore, we investigate convergence and computational complexity for such algorithms and illustrate their performance by a numerical example.