The Least Square Solution to an Overdetermined System
Theory and Applications
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Beschreibung
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.
Provide a practically applicable theory using only elementary linear algebra Deliver essential ideas for developing mathematics with real-world applications Introduce compelling practical applications across engineering and technology
Autor*in
Takashi Takiguchi
Themen in »The Least Square Solution to an Overdetermined System«
least square solution system of overdetermined linear equations correction of measurements non-destructive inspection inverse problems medical imaging