Symbolic-numeric nonlinear equation solving
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
ACM Transactions on Mathematical Software (TOMS)
Interval Analysis on Directed Acyclic Graphs for Global Optimization
Journal of Global Optimization
Efficient interval partitioning-Local search collaboration for constraint satisfaction
Computers and Operations Research
Efficient interval partitioning for constrained global optimization
Journal of Global Optimization
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Constraint propagation on quadratic constraints
Constraints
Direct method for solving parametric interval linear systems with non-affine dependencies
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
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Interval iteration can be used, in conjunction with othertechniques, for rigorously bounding all solutions to a nonlinear systemof equations within a given region, or for verifying approximatesolutions. However, because of overestimation which occurs when theinterval Jacobian matrix is accumulated and applied, straightforwardlinearization of the original nonlinear system sometimes leads tononconvergent iteration.In this paper, we examine interval iterations based on an expandedsystem obtained from the intermediate quantities in the original system.In this system, there is no overestimation in entries of the intervalJacobi matrix, and nonlinearities can be taken into account to obtainsharp bounds. We present an example in detail, algorithms, and detailedexperimental results obtained from applying our algorithms to theexample.—Author's Abstract