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SIAM Journal on Mathematics of Data Science 2, 658 (2020)

Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions

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SIAM Rev. 62, 617 (2020)

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

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SIAM Rev. 62, 661 (2020)

Why Are U.S. Parties So Polarized? A “Satisficing” Dynamical Model

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On the Ruin Problem with Investment When the Risky Asset Is a Semimartingale

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## Featured Books

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Theory and Numerical Approximations of Fractional Integrals and Derivatives

The book's core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.

Fast Direct Solvers for Elliptic PDEs

This textbook provides an introduction to such solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling the dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. The book also describes modern linear algebraic techniques that accelerate computations, such as randomized algorithms, interpolative decompositions, and data- sparse and rank-structured hierarchical matrix representations.

Practical Optimization

In the intervening years since this book was published in 1981, the field of optimization has been exceptionally lively. This fertility has involved not only progress in theory, but also faster numerical algorithms and extensions into unexpected or previously unknown areas such as semidefinite programming. Despite these changes, many of the important principles and much of the intuition can be found in this Classics version of Practical Optimization.

An Introduction to Compressed Sensing

Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing.

Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition

This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice René Fréchet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical differential calculus, including the chain rule, making it a natural framework for initiating a large audience of undergraduates and non-mathematicians into the world of nondifferentiable optimization.

Piecewise Affine Control: Continuous Time, Sampled Data, and Networked Systems

This book targets controller design for piecewise affine systems, fulfilling both performance and stability requirements. It presents a unified computational methodology for the analysis and synthesis of piecewise affine controllers, and introduces algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems. Examples from several areas are featured.

Complex Variables and Analytic Functions: An Illustrated Introduction

At almost all academic institutions worldwide, complex variables and analytic functions are utilized in courses on applied mathematics, physics, engineering, and other related subjects. For most students, formulas alone do not provide a sufficient introduction to this widely taught material, yet illustrations of functions are sparse in current books on the topic. This is the first primary introductory textbook on complex variables and analytic functions to make extensive use of functional illustrations.

Interpolatory Methods for Model Reduction

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response..

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