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. 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--Publisher website "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."--Page 4 de la couverture 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 Bibliography Most existing textbooks on this subject were written either for mathematics or engineering students and do not address the unique situation of computer science students, who have some background in discrete mathematics but less familiarity with continuous methods of proof and algorithms. This book is written specifically for those students, filled throughout with practical examples using the algorithms being taught. The book also teaches theory in the context of application in parallel by delving into real-world problems in computer graphics and computer vision.