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"This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigor, it advances readers understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms."

"The presentation is designed to guide new users through the basics of interacting with and programming in the MATLAB software, while also presenting some of its more important and advanced techniques, including how to solve common problem types in scientific computing. Rather than including exhaustive technical material, the author teaches through readily understood examples and numerous exercises that range from straightforward to very challenging. Readers are encouraged to learn by doing: entering the examples themselves, reading the online help, and trying the exercises."

"This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations. Originally published in 1987, it remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for high-school and undergraduate mathematics projects."

"A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods."

"This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years. An update of Ramon Moore previous books on the topic, it provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis. The authors provide a hands-on introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB. Readers will find the following features of interest: elementary motivating examples and notes that help maximize the reader chance of success in applying the techniques; exercises and hands-on MATLAB-based examples woven into the text; INTLAB-based examples and explanations integrated into the text, along with a comprehensive set of exercises and solutions, and an appendix with INTLAB commands; an extensive bibliography and appendices that will continue to be valuable resources once the reader is familiar with the subject; and a Web page with links to computational tools and other resources of interest."

"separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions. Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming. Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful self-contained appendices on vectors and matrices, topological properties of n-dimensional real space, continuity and minimization, and differentiable functions."

"Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993.Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices. On the way, semigroups of nonnegative matrices and symmetric nonnegative matrices are discussed. Later, applications of nonnegativity and M-matrices are given; for numerical analysis the example is convergence theory of iterative methods, for probability and statistics the examples are finite Markov chains and queuing network models, for mathematical economics the example is input-output models, and for mathematical programming the example is the linear complementarity problem.Nonnegativity constraints arise very naturally throughout the physical world. Engineers, applied mathematicians, and scientists who encounter nonnegativity or generalizations of nonegativity in their work will benefit from topics covered here, connecting them to relevant theory. Researchers in one area, such as queuing theory, may find useful the techniques involving nonnegative matrices used by researchers in another area, say, mathematical programming."

"Solutions of the wave equation or Maxwell's equations in boundary value and free space problems are analyzed. Hyperbolic systems in domains going off to infinity are studied. New results on Maxwell's equations and non-star shaped reflecting bodies are included."

"Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study."

"Flow control and optimization has been an important part of experimental flow science throughout the last century. As research in computational fluid dynamics (CFD) matured, CFD codes were routinely used for the simulation of fluid flows. Subsequently, mathematicians and engineers began examining the use of CFD algorithms and codes for optimization and control problems for fluid flows. The marriage of mature CFD methodologies with state-of-the-art optimization methods has become the center of activity in computational flow control and optimization.Perspectives in Flow Control and Optimization presents flow control and optimization as a subdiscipline of computational mathematics and computational engineering. It introduces the development and analysis of several approaches for solving flow control and optimization problems through the use of modern CFD and optimization methods. The author discusses many of the issues that arise in the practical implementation of algorithms for flow control and optimization, such as choices to be made and difficulties to overcome. He provides the reader with a clear idea of what types of flow control and optimization problems can be solved, how to develop effective algorithms for solving such problems, and potential problems to be aware of when implementing the algorithms.This book is written for both those new to the field of control and optimization as well as experienced practitioners, including engineers, applied mathematicians, and scientists interested in computational methods for flow control and optimization. Both those interested in developing new algorithms and those interested in the application of existing algorithms should find useful information in this book."