A reduced Newton method for constrained linear least-squares problems
نویسندگان
چکیده
منابع مشابه
A reduced Newton method for constrained linear least-squares problems
We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally...
متن کاملLinearized Alternating Direction Method for Constrained Linear Least-squares Problem
In this paper, we apply the alternating direction method (ADM) to solve a constrained linear least-squares problem where the objective function is a sum of two least-squares terms and the constraints are box constraints. Using ADM, we decompose the original problem into two easier least-squares subproblems at each iteration. To speed up the inner iteration, we linearize the subproblems whenever...
متن کاملLinear Least Squares Problems
A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...
متن کاملConvexly constrained linear inverse problems: iterative least-squares and regularization
| In this paper, we consider robust inversion of linear operators with convex constraints. We present an iteration that converges to the minimum norm least squares solution; a stopping rule is shown to regularize the constrained inversion. A constrained Laplace inversion is computed to illustrate the proposed algorithm.
متن کاملStochastic Newton and Quasi-Newton Methods for Large Linear Least-squares Problems
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity is introduced in two different frameworks as a means to overcome these compu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2010
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.10.006