On Solving Large-Scale Weighted Least Squares Problems
نویسنده
چکیده
A sequence of least squares problems of the form miny kG 1=2 (A T y ? h)k2 where G is an n n positive deenite diagonal weight matrix, and A an m n (m < n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We discuss a technique for forming low-rank correction pre-conditioners for such problems. Finally we give numerical results to illustrate this technique.
منابع مشابه
Large Scale Experiments Data Analysis for Estimation of Hydrodynamic Force Coefficients Part 1: Time Domain Analysis
This paper describes various time-domain methods useful for analyzing the experimental data obtained from a circular cylinder force in terms of both wave and current for estimation of the drag and inertia coefficients applicable to the Morison’s equation. An additional approach, weighted least squares method is also introduced. A set of data obtained from experiments on heavily roughened circul...
متن کاملLarge-Scale Optimization Methods with Application to Design of Filter Networks
Nowadays, large-scale optimization problems are among those most challenging. Any progress in developing methods for large-scale optimization results in solving important applied problems more effectively. Limited memory methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the...
متن کاملApplication of a Class of Preconditioners to Large Scale Linear Programming Problems
In most interior point methods for linear programming, a sequence of weighted linear least squares problems are solved, where the only changes from one iteration to the next are the weights and the right hand side. The weighted least squares problems are usually solved as weighted normal equations by the direct method of Cholesky factoriza-tion. In this paper, we consider solving the weighted n...
متن کاملFast solving of weighted pairing least-squares systems
This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods, suitable for solving full rank systems as well as rank deficient systems, are studied. Computational experiments clearly show that the best method, in terms of spee...
متن کاملA highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems∗
We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the `1-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of solvers in the literature for the Lasso problems, we found that no solver can efficiently handle difficult large scale regression problems with real data. By lever...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000