With a renewed interest in robotics and the advent of big data, numerical algorithms for machine vision, machine learning, and data analysis are becoming increasingly important. Linear algebra and calculus serve as the foundation for many of these algorithms. Having a sound knowledge of this field of mathematics is, therefore, critical for any student of computer science who is interested in robotics or wishes to work with big data.

This book is organized into four sections and 16 chapters. The first section, comprising chapters 1 and 2, covers the basic concepts and serves as a refresher for those who have been away from or have not used these concepts since a high school or undergraduate course in linear algebra and calculus. It also covers concepts that distinguish numerical from discrete algorithms. Chapters 3 through 7 make up Section 2 and cover algorithms that involve solving linear systems of equations with a wide range of applications in data analysis, image processing, and face recognition. Nonlinear optimization techniques, widely used in machine learning, are the focus of chapters 8 through 12 in Section 3. While the algorithms in the previous sections largely provide solutions to unknown points, algorithms in chapters 13 through 16 of Section 4 provide solutions to unknown functions. These algorithms have applications in computational physics, 3D rendering, x-ray scanning, and geometry processing.

Numerical algorithms challenges its readers and is not for the faint of heart. Each section starts out with key concepts established in the field and gradually builds up to more advanced topics from recent research. End-of-chapter exercises are nontrivial; one needs to go through the material in each chapter at a gradual pace and reflect on the material before fully grasping their essence. The book is suitable for advanced undergraduate or early graduate students of computer science who have a keen interest in robotics and big data analysis. It is also a good resource for instructors looking to develop advanced courses in these areas.

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