Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians. In this second edition, the material on...

Offers an overview of the MM principle, a device for deriving optimization algorithms satisfying the ascent or descent property. These algorithms can:Separate the variables of a problem. Avoid large matrix inversions. Linearize a problem. Restore symmetry.Deal with equality and inequality constraints gracefully. Turn a non-differentiable problem into a smooth problem.The author: Presents the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics. Derives numerous algorithms from a broad diversity of...

Algorithms are a dominant force in modern culture, and every indication is that they will become more pervasive, not less. The best algorithms are undergirded by beautiful mathematics. This text cuts across discipline boundaries to highlight some of the most famous and successful algorithms. Readers are exposed to the principles behind these examples and guided in assembling complex algorithms from simpler building blocks. Algorithms from THE BOOK: Incorporates Julia code for easy experimentation. Is written in clear, concise prose consistent with mathematical rigour. Includes a...