EXPLORATIONS NUMERICAL ANALYSIS & MACHINE LEARN WITH JULIA

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).

Contents:

• Preface
• Preliminaries:
  • Introduction
  • Julia Primer
  • Understanding Error
• Numerical Linear Algebra:
  • Direct Methods for Linear Systems
  • Least Squares Problems
  • Iterative Methods for Linear Systems
  • Eigenvalue Problems
• Data Fitting and Function Approximation:
  • Polynomial Interpolation
  • Approximation of Functions
  • Differentiation and Integration
• Nonlinear Equations and Optimization:
  • Zeros of Nonlinear Functions
  • Optimization
• Differential Equations:
  • Initial Value Problems
  • Two-Point Boundary Value Problems
  • Partial Differential Equations
• Machine Learning:
  • Elements of Machine Learning
  • Classification and Regression
  • Deep Learning Networks
• Appendices:
  • Review of Calculus
  • Review of Linear Algebra
• Bibliography
• Index

Readership: Advanced undergraduate or beginning graduate students in mathematics. Researchers in science and engineering fields who require a working knowledge of numerical methods or machine learning techniques.