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 ......
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 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 ......
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 ......
This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed ......
A Comprehensive Introduction to Modeling, Analysis, Simulation, Applications
Historically, optimal transport was about moving a pile of mortar efficiently or transferring the output of an array of steel mines optimally. This type of problem has been found to arise in many different fields of mathematics, science, and engineering-from fluid dynamics to many-electron physics to artificial intelligence-and in the last three ......
This book provides the mathematical foundations needed for designing practical controllers for linear time-invariant systems. The authors accomplish this by incorporating intentional time delays into measurements with the goal of achieving anticipation capabilities, reduction in noise sensitivity, and a fast response. The benefits of these types ......
