A Cramer rule for least-norm solutions of consistent linear equations

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

A Distributed Algorithm for Least Square Solutions of Linear Equations

A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive information from its nearby neighbors. For fixed, connected, and undirected networks, the proposed discrete-time algorithm results in each agents solution estimate to...

least squares solutions of inconsistent fuzzy linear matrix equations

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least squares solutions of inconsistent fuzzy linear matrix equations

A fast algorithm for computing minimal-norm solutions to underdetermined systems of linear equations

We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank matrix Am×n with m < n, any vector bm×1, and any positive real number ε less than 1, the procedure computes a vector xn×1 approximating to relative precision ε or better the vector pn×1 of minimal Euclidean norm satisfying Am×n pn×1 = bm×1. T...