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
12 - Optimization and Root Finding of Algebraic Systems
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
Optimization and root finding are closely aligned techniques for determining the extremums and zeros, respectively, of a function.Newton's method is the workhorse of both types of algorithms for nonlinear functions, and the conjugate-gradient and GMRES methods are also covered.Optimization of linear, quadratic, and nonlinear functions are addressed with and without constraints, which may be equality or inequality.In the linear programming case, emphasis is placed on the simplex method.
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- Publisher: Cambridge University PressPrint publication year: 2021