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 topicsâ€”from numerical linear algebra to optimization and differential equationsâ€”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 studentsâ€™ 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
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.
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 Princetonâ€™s Program in Applied and Computational Mathematics. Before his graduate studies, he was a member of Pixarâ€™s Tools Research group.
"This book covers an impressive array of topics, many of which are paired with a real-world application. Its conversational style and relatively few theorem-proofs make it well suited for computer science students as well as professionals looking for a refresher."
â€”Dianne Hansford, FarinHansford.com