Journal ArticleDOI
Algorithms for separable nonlinear least squares problems
Axel Ruhe,Per Åke Wedin +1 more
TLDR
In this paper, an iterative Gauss-Newton algorithm for solving nonlinear least squares problems is proposed, where the variables are separated into two sets in such a way that in each iteration, optimization with respect to the first set is performed first, and corrections to those of the second after that.Abstract:
Iterative algorithms of Gauss–Newton type for the solution of nonlinear least squares problems are considered. They separate the variables into two sets in such a way that in each iteration, optimization with respect to the first set is performed first, and corrections to those of the second after that. The linear-nonlinear case, where the first set consists of variables that occur linearly, is given special attention, and a new algorithm is derived which is simpler to apply than the variable projection algorithm as described by Golub and Pereyra, and can be performed with no more arithmetical operations than the unseparated Gauss–Newton algorithm. A detailed analysis of the asymptotical convergence properties of both separated and unseparated algorithms is performed. It is found that they have comparable rates of convergence, and all converge almost quadratically for almost compatible problems. Simpler separation schemes, on the other hand, converge only linearly. An efficient and simple computer impleme...read more
Citations
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Journal ArticleDOI
Separable nonlinear least squares: the variable projection method and its applications
Gene H. Golub,Victor Pereyra +1 more
TL;DR: In this paper, the authors review 30 years of developments and applications of the variable projection method for solving separable nonlinear least-squares problems and present a variety of applications from electrical engineering, medical and biological imaging, chemistry, robotics, vision, and environmental sciences.
Journal ArticleDOI
Detection and estimation in sensor arrays using weighted subspace fitting
TL;DR: In this article, a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed, based on the recently introduced weighted subspace fitting (WSF) criterion and includes schemes for detecting the number of sources and estimating the signal parameters.
Journal ArticleDOI
A paraperspective factorization method for shape and motion recovery
Conrad J. Poelman,Takeo Kanade +1 more
TL;DR: This work has shown that the paraperspective factorization method can be applied to a much wider range of motion scenarios, including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low-altitude airplane.
Journal ArticleDOI
Sufficient Dimension Reduction via Inverse Regression
R. Dennis Cook,Liqiang Ni +1 more
TL;DR: In this article, the inverse regression estimator (IRE) is proposed, along with inference methods and a computational algorithm, which has at least three desirable properties: (1) its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an as-ymptotic chi-squared distribution, and (3) it provides a chi-quared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors.
Journal ArticleDOI
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
TL;DR: This work forms the B-spline curve fitting problem as a nonlinear least squares problem and concludes that SDM is a quasi-Newton method which employs a curvature-based positive definite approximant to the true Hessian of the objective function.
References
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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
Nonmetric multidimensional scaling: A numerical method
TL;DR: The numerical methods required in the approach to multi-dimensional scaling are described and the rationale of this approach has appeared previously.
Journal ArticleDOI
The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.
Gene H. Golub,Victor Pereyra +1 more
TL;DR: Algorithms are presented which make extensive use of well-known reliable linear least squares techniques, and numerical results and comparisons are given.
Journal ArticleDOI
A Method for Separable Nonlinear Least Squares Problems with Separable Nonlinear Equality Constraints
Linda Kaufman,Victor Pereyra +1 more
TL;DR: In this article, the authors extend these techniques to the separable nonlinear least squares problem subject to separable nonsmooth equality constraints, where the nonlinear variables only have a solution whose solution is the solution to the original problem.
Related Papers (5)
The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.
Gene H. Golub,Victor Pereyra +1 more
The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate.
G. H. GOLUBf,V. Pereyra +1 more