Description:
The textbook is an expansion of Explorations in Numerical Analysis that includes new chapters covering topics from machine learning. It is intended for advanced undergraduate and early graduate students, with a focus on the connections between numerical analysis and machine learning.
Topics covered include computer arithmetic, error analysis, solution of systems of linear equations by direct and iterative methods, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, partial differential equations, machine learning, classification, regression, and neural networks.
Each problem is presented with derivations of solution techniques, analysis of their efficiency, accuracy and robustness, and detailed implementation using the Julia programming language. This book is suitable for a year-long course in numerical analysis, or for a one-semester course in numerical linear algebra (Part II) or machine learning (Part VI).