The Least Square Solution to an Overdetermined System : Theory and Applications.

Format:

Book

Author/Creator:

Takiguchi, Takashi., author.

Series:

SpringerBriefs in Applied Sciences and Technology Series

Language:

English

Physical Description:

1 online resource (136 pages)

Edition:

1st ed.

Place of Publication:

Singapore : Springer, 2026.

Summary:

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.

Contents:

SpringerBriefs in Applied Sciences and Technology

The Least Square Solution to an Overdetermined System

Preface

Acknowledgments

Contents

1. Introduction

2. Structure and Approximation of the Solutions to Overdetermined Systems

3. Examples of Practical Applications

4. Structure of the Accuracy and the Inaccuracy of the Least-Square Solutions

5. A Method to Construct an Approximate Solution to an Overdetermined System

6. Theoretical Proofs of How Approximate the Least-Square Solution is to the Real One

7. A Theoretical Study of the Algorithm for CT by G. N. Hounsfield

8. Ultrasonic Imaging (USI)

Appendix A

Review of Elementary Linear Algebra

Solutions to the Exercises and with Comments

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

References

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819200641