A row space method for solving a system of linear equations
Michael F. Zimmer
TL;DR
This paper introduces a novel row space algorithm for directly solving consistent linear systems, providing minimum norm solutions, generalized inverses, and null space projections with an online computation feature.
Contribution
It presents a new algorithm that avoids triangular system solutions and block matrices, enabling efficient, online computation of solutions to linear systems.
Findings
Computes minimum norm solutions and generalized inverses.
Supports online data processing for linear systems.
Does not require triangular or block matrix solutions.
Abstract
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In addition, the algorithm permits an online formulation so that computations may proceed as the data become available. The algorithm does not require the solution of a triangular system of equations, nor does it rely on block partitioned matrices.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Numerical Methods and Algorithms