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Provides an in-depth treatment of sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.

Based on a master's program course at the University of Southern California, the main goal of Mathematics and Tools for Financial Engineering is to train students to use mathematical and engineering tools to understand and solve financial problems. The book contains numerous examples and problem

Introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations.

Provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient.

Presents a special solution of underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called sparse solution. As underdetermined linear systems can be very different, the authors explain how to compute a sparse solution by many approaches.

Combines nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential/differential-algebraic equations to solve optimal control problems.

Interpolatory methods are among the most widely used model reduction techniques. This book is the first comprehensive analysis of this approach available in a single, extensive resource. It covers both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.

Aiming to reach undergraduate students entering the world of complex variables and analytic functions, this book utilizes graphics to visually build on familiar cases and illustrate how these same functions extend beyond the real axis. It covers several important topics that are omitted in nearly all recent texts.

The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems.

How to study the stability of dynamical systems influenced by time delays is a fundamental question. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems addresses this question for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques.

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modelling issues and to some of the latest developments in these areas.

Provides basic, essential knowledge of some of the tools of real analysis: the Hardy-Littlewood maximal operator, the Calderon-Zygmund theory, the Littlewood-Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various difficulties designed to challenge and engage students

Provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well.

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks.

Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition.

This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.

This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.

This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity. There is also added material on checkpointing and iterative differentiation.

Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.

Covers the fundamentals of the theory of ordinary differential equations.

This is the only book available that analyses in depth the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis.