Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and iterative methods for solving systems of linear equations. Systematic methods and rigorous theory on ......
This book is a self-contained introduction to quantum algorithms with an emphasis on quantum optimization, that is, quantum algorithms to solve optimization problems. The book provides all the tools necessary to understand the benefits and drawbacks of quantum optimization algorithms, paying particular attention to provable guarantees and ......
This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical ......
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 ......
Moment and polynomial optimization is an active research field used to solve difficult questions in many areas, including global optimization, tensor computation, saddle points, Nash equilibrium, and bilevel programs, and it has many applications. The author synthesizes current research and applications, providing a systematic introduction to ......
One of the most popular ways to assess the "effort" needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions-and given access to problem-function values and ......
Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional ......
Iterative methods use successive approximations to obtain more accurate solutions. Iterative Methods and Preconditioners for Systems of Linear Equations presents historical background, derives complete convergence estimates for all methods, illustrates and provides Matlab codes for all methods, and studies and tests all preconditioners first as ......
Lectures on Stochastic Programming: Modeling and Theory, Third Edition covers optimization problems involving uncertain parameters for which stochastic models are available. These problems occur in almost all areas of science and engineering. This substantial revision of the previous edition presents a modern theory of stochastic programming, ......
