Takashi Takiguchi – författare

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.

This book comprises select proceedings of the workshop “Practical inverse problems and their prospects” held online by zoom, from Mar 2nd to Mar. 4th, 2022, supported by Institute of Mathematics for Industry, Kyushu University focusing on cutting-edge research carried out in the areas of practical inverse problems based on industry-academia and interdisciplinary collaborations.Various themes on practical inverse problems covered in this book are medical imaging, non-destructive and non-invasive inspections, viscoelastic waves, remote sensing, infrared light tomography, maintenance of infrastructure, and so on, and mathematical theories in inverse problems are also handled in these proceedings.All papers in this book are written by qualified authors in the practical inverse problems area and also the papers are newly announced. Readers can get leading-edge information on practical inverse problems.