A modular system of algorithms for unconstrained minimization
ACM Transactions on Mathematical Software (TOMS)
Approximate solution of the trust region problem by minimization over two-dimensional subspaces
Mathematical Programming: Series A and B
Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers
Local convergence analysis of tensor methods for nonlinear equations
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
ACM Transactions on Mathematical Software (TOMS)
A quartic nonlinear optimization method
Neural, Parallel & Scientific Computations
Solvers for Nonlinear Algebraic Equations; Where Are We Today?
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Solvers for Systems of Nonlinear Algebraic Equations - Their Sensitivity to Starting Vectors
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Quadratic backward propagation of variance for nonlinear statistical circuit modeling
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
EFCOSS: An interactive environment facilitating optimal experimental design
ACM Transactions on Mathematical Software (TOMS)
Original article: A quantitative metric for robustness of nonlinear algebraic equation solvers
Mathematics and Computers in Simulation
Hi-index | 0.00 |
This article describes a modular solftware package for solving systems of nonlinear equations and nonlinear problems, using a new class of methods called tensor methods. It is intended for small- to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or to approximate it by finite differences at each iteration. The software allows the user to choose between a tensor method and a standard method based on a linear model. The tensor method approximates F(x) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies: a line search approach and a two-dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small- and medium-sized problems in iterations and function evaluations.