Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into the theoretical tools needed to support these skills.

The book covers a wide range of topics―from numerical linear algebra to optimization and differential equations―focusing on real-world motivation and unifying themes. It incorporates cases from computer science research and practice, accompanied by highlights from in-depth literature on each subtopic. Comprehensive end-of-chapter exercises encourage critical thinking and build students’ intuition while introducing extensions of the basic material.

The text is designed for advanced undergraduate and beginning graduate students in computer science and related fields with experience in calculus and linear algebra. For students with a background in discrete mathematics, the book includes some reminders of relevant continuous mathematical background.

Table of Contents

Section I: Preliminaries
Chapter 1: Mathematics Review
Chapter 2: Numerics and Error Analysis

Section II: Linear Algebra
Chapter 3: Linear Systems and the LU Decomposition
Chapter 4: Designing and Analyzing Linear Systems
Chapter 5: Column Spaces and QR
Chapter 6: Eigenvectors
Chapter 7: Singular Value Decomposition

Section III: Nonlinear Techniques
Chapter 8: Nonlinear Systems
Chapter 9: Unconstrained Optimization
Chapter 10: Constrained Optimization
Chapter 11: Iterative Linear Solvers
Chapter 12: Specialized Optimization Methods

Section IV: Functions, Derivatives, and Integrals
Chapter 13: Interpolation
Chapter 14: Integration and Differentiation
Chapter 15: Ordinary Differential Equations
Chapter 16: Partial Differential Equations