NUMERICAL ALGORITHMS: METHODS FOR COMPUTER VISION, MACHINE LEARNING, AND GRAPHICS

Preliminaries
• Mathematics Review
• Numerics and Error Analysis
• Linear Algebra. Linear Systems and the LU Decomposition
• Designing and Analyzing Linear Systems
• Column Spaces and QR
• Eigenvectors
• Singular Value Decomposition
• Nonlinear Techniques. Nonlinear Systems
• Unconstrained Optimization
• Constrained Optimization
• Iterative Linear Solvers
• Specialized Optimization Methods
• Functions, Derivatives, and Integrals. Interpolation
• Integration and Differentiation
• Ordinary Differential Equations
• Partial Differential Equations
Exercises appear at the end of each chapter.

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.

Features
• Contains classroom-tested material for a one- to two-semester course in numerical algorithms, with a focus on modeling and applications
• Introduces themes common to nearly all classes of numerical algorithms
• Covers algorithms for solving linear and nonlinear problems, including popular techniques recently introduced in the research community
• Includes comprehensive end-of-chapter exercises that push students at all levels to derive, extend, and analyze numerical algorithms
Solutions manual and figure slides available upon qualifying course adoption

Author
Justin Solomon is an assistant professor in the Department of Electrical Engineering and Computer Science at MIT, where he studies problems in shape analysis, machine learning, and graphics from a geometric perspective. He received a PhD in computer science from Stanford University, where he was also a lecturer for courses in graphics, differential geometry, and numerical methods. Subsequently he served as an NSF Mathematical Sciences Postdoctoral Fellow at Princeton’s Program in Applied and Computational Mathematics. Before his graduate studies, he was a member of Pixar’s Tools Research group.