Year: 2016
Type: preprint
Abstract: A system of linear equations is normally understood as a linear mapping between two vector spaces. However, most direct solutions (e.g., QR, LU, ...) rely on the inelegant approach of back-substitution: a significant departure from such a characterization. In this paper, two new methods are introduced which respect the underlying vector space throughout, whether it be the row or column space of the coefficient matrix. Both solutions produce a generalized inverse as well as a projection operator for the null space. They also have the unique feature of admitting an online solution, which allows a solution to be computed as the data becomes available.
Source: arXiv (Cornell University)
Author: Zimmer, Michael F.
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3090108352