A resurgence of interest in network synthesis in the last decade, motivated in part by the introduction of the inerter, has led to the need for a better understanding of the most economical way to realize a given passive impedance. This monograph outlines the main contributions to the field of passive network synthesis and presents new research ......
Perturbation methods are old and powerful. Solutions are provided as formulas rather than numbers or pictures, so the skill of the person (or machine!) reading the formula is essential. This unique book presents several classical methods to solve perturbation problems using backward error analysis. This lessens the likelihood of blunders because ......
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 ......
And Related Problems of Mathematical Physics, Engineering, and Life Sciences
This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations (ODEs) using power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured ......
This book addresses an important class of problems in the field of mathematical optimization- - those involving nonconvex and/or nonsmooth continuous functions. The authors introduce the theoretical foundations of nonconvex nonsmooth functions and discuss optimality conditions for optimization problems involving such functions. They also provide ......
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 ......
