Including One Theorem, One Rule of Thumb, and One Hundred and Six Exercises
This book provides an easily accessible, yet detailed, discussion of computer arithmetic as mandated by the IEEE 754 floating point standard, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and industry, the standard is supported by virtually every ......
Most books on algorithms are narrowly focused on a single field of application. This unique book cuts across discipline boundaries, exposing readers to the most successful algorithms from a variety of fields. Algorithm derivation is a legitimate branch of the mathematical sciences driven by hardware advances and the demands of many scientific ......
Matrix eigenvalue problems arise in a wide variety of fields in science and engineering, so it is important to have reliable and efficient methods for solving them. Of the methods devised, bulge-chasing algorithms, such as the famous QR and QZ algorithms, are the most important. This book focuses on pole-swapping algorithms, a new class of methods ......
This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are ......
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference ......
This comprehensive book focuses on numerical methods for approximating solutions to partial differential equations. Intended as a broad survey of methods, the aim is to introduce readers to the central concepts of various families of discretizations and solution algorithm and lay the foundation needed to understand more advanced material, The book ......
Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for solving evolutionary PDEs, particularly in the fields of hyperbolic and kinetic equations. The ......
This book is a continuation of the author's earlier book Spline Functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the last ten years that make use of splines to approximate functions and data and to solve boundary-value problems. The first half of the book works with bivariate ......
Navier-Stokes equations are one of the most impactful techniques for modeling physical flow phenomena. The coupling of velocity and pressure, along with the nonlinearity, is a challenge for the mathematical and numerical analysis of these equations. This self-contained book provides a thorough theoretical study of finite element methods for ......
