Linear Least Squares Problems

Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

Solving Rank-Deficient Linear Least-Squares Problems*

Numerical solution of linear least-squares problems is a key computational task in science and engineering. Effective algorithms have been developed for the linear least-squares problems in which the underlying matrices have full rank and are well-conditioned. However, there are few efficient and robust approaches to solving the linear least-squares problems in which the underlying matrices are...

A meshless discrete Galerkin method for solving the universe evolution differential equations based on the moving least squares approximation

In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

An Effective Hybrid Artificial Bee Colony Algorithm for Nonnegative Linear Least Squares Problems

An effective hybrid artificial bee colony algorithm is proposed in this paper for nonnegative linear least squares problems. To further improve the performance of algorithm, orthogonal initialization method is employed to generate the initial swarm. Furthermore, to balance the exploration and exploitation abilities, a new search mechanism is designed. The performance of this algorithm is verifi...

Estimates of Optimal Backward Perturbations for Linear Least Squares Problems∗

Numerical tests are used to validate a practical estimate for the optimal backward errors of linear least squares problems. This solves a thirty-year-old problem suggested by Stewart and Wilkinson.