Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- Part III Least Squares and Optimization
- 10 Least-Squares Methods
- 11 Data Analysis: Curve Fitting and Interpolation
- 12 Optimization and Root Finding of Algebraic Systems
- 13 Data-Driven Methods and Reduced-Order Modeling
- References
- Index
10 - Least-Squares Methods
from Part III - Least Squares and Optimization
Published online by Cambridge University Press: 18 February 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Matrix Methods
- Part II Numerical Methods
- Part III Least Squares and Optimization
- 10 Least-Squares Methods
- 11 Data Analysis: Curve Fitting and Interpolation
- 12 Optimization and Root Finding of Algebraic Systems
- 13 Data-Driven Methods and Reduced-Order Modeling
- References
- Index
Summary
Least-squares methods provide the mathematical foundation for optimization of algebraic systems.They can be applied to overdetermined systems, having more equations than unknowns, or undertermined systems, having fewer equations than unknowns.The optimization may involve constraints or be subject to a penalty function.Numerical methods, namely the conjugate-gradient and GMRES methods, that are based on least-squares optimization method are discussed in detail and put into the context of other Krylov-based methods.
Keywords
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2021