Takiguchi The Least Square Solution to an Overdetermined System

Theory and Applications
1. Auflage 2026
ISBN: 978-981-9200-64-1
Verlag: Springer Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 84 Seiten

Reihe: SpringerBriefs in Mathematical Methods

This book addresses a gap in elementary linear algebra: while solving systems of linear equations with multiple solutions is standard, analyzing overdetermined systems with no solution—common in practical applications—is rarely taught. We develop a theory for such systems using the concept of least-squares solutions, grounded entirely in elementary linear algebra. Unlike approaches based on the Moore–Penrose inverse, which require advanced tools such as singular value decomposition, our method relies only on basic principles yet performs effectively in real-world contexts. Practical applications include non-destructive inspection of concrete structures, GNSS-based position detection, and the implementation of computerized tomography. Designed as a monograph for researchers and educators, this book can also serve as a graduate or advanced undergraduate textbook for students interested in applied mathematics. It is equally suitable for senior undergraduate research projects and for engineers seeking accessible mathematical tools for practical problems.

Zielgruppe

Research

Autoren/Hrsg.

Takiguchi, Takashi

Inhaltsverzeichnis

Introduction; motivation of this monograph.- General theory of least square solutions to an overdetermined system of linear equations with no solution.- Semi-equivalent systems to overdetermined systems of linear equations with no solution.- Practical applications.- Similar ideas to analyze an overdetermined system of linear equations with no solution.

Über Autor(innen)

Takashi Takiguchi is an associate professor at National Defense Academy of Japan.