Journal ArticleDOI
An algorithm for solving sparse nonlinear least squares problems
TLDR
A new method for solving Nonlinear Least Squares problems when the Jacobian matrix of the system is large and sparse using a preconditioned Conjugate Gradient algorithm and a two-dimensional trust region scheme is introduced.Abstract:
We introduce a new method for solving Nonlinear Least Squares problems when the Jacobian matrix of the system is large and sparse.read more
Citations
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Journal ArticleDOI
On a class of nonlinear equation solvers based on the residual norm reduction over a sequence of affine subspaces
Igor E. Kaporin,Owe Axelsson +1 more
TL;DR: A brake control system for vehicles in which the difference in speed of rotation of a corresponding pair of wheels is detected in a prebraking mode of operation, and if the differences in rotational speed exceeds a predetermined amount, the brakes on the pair of Wheels are disabled.
Journal ArticleDOI
Advances in trust region algorithms for constrained optimization
TL;DR: A survey of recent advances in trust region algorithms is presented and the different choices of penalty function, Lagrange function and expanded Lagrangian function used for modeling constrained optimization problems and solving these equations usingtrust region algorithms are explained.
Journal ArticleDOI
A parallel projection method for overdetermined nonlinear systems of equations
TL;DR: A generalization of the classical method of Cimmino for linear systems for overdetermined nonlinear systems and a practical strategy for improving the global convergence properties of the method are introduced.
Journal ArticleDOI
An algorithm for solving nonlinear least-squares problems with a new curvilinear search
José Mario Martínez,F. F. Santos +1 more
TL;DR: In this article, a modification of an algorithm introduced by Martinez (1987) for solving nonlinear least-squares problems is proposed, which simplifies the process of searching the new point and defines the plane using a scaled gradient direction, instead of the original gradient.
Journal ArticleDOI
A numerically stable reduced-gradient type algorithm for solving large-scale linearly constrained minimization problems
TL;DR: A reduced-gradient type algorithm for solving large-scale linearly constrained minimization problems using a preconditioned conjugate-gradient scheme that provides numerical stability and total storage may be predicted before beginning the calculations.
References
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Journal ArticleDOI
A method for the solution of certain non – linear problems in least squares
TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.
Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.