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 book develops the theory of probability and mathematical statistics with the goal of analyzing real-world data. Throughout the text, the R package is used to compute probabilities, check analytically computed answers, simulate probability distributions, illustrate answers with appropriate graphics, and help students develop intuition ......
The book presents a solution to a problem in adaptive control design that was open for 40 years: robustification of disturbances without compromising asymptotic performance. This original methodology builds on foundational ideas, such as the use of a deadzone in the update law and nonlinear damping in the controller, and advances the tools for and ......
Rounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices. A detailed analysis is given of the rounding errors made in the elementary arithmetic operations and inner products, for both floating-point arithmetic and ......
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem ......
Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools-algebraic geometry, algebraic combinatorics, and representation theory, among others-are ......
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 ......
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces ......
