Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in ......
Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs - and the requirement for rapid solution - pose significant difficulties. A particularly challenging class of PDE-constrained ......
This book provides a comprehensive introduction to the mathematical methodology of parameter continuation, the computational analysis of families of solutions to nonlinear mathematical equations. It develops a systematic formalism for constructing abstract representations of continuation problems and for implementing these in an existing ......
Survival data typically consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. In contrast, many applications involve repeated-events data, where a sample unit may accumulate any number of events over time. Examples include the number and cost of repairs of products, the number and ......
This book is composed of eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameters systems. Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems ......
This book covers and expands upon material presented by the author at a CBMS-NSF Regional Conference during a ten-lecture series on multiphase flows in porous media and their simulation. It begins with an overview of classical reservoir engineering and basic reservoir simulation methods and then progresses through a discussion of types of flows - ......
This book addresses an important class of mathematical problems (the Riemann problem) for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. It covers the fundamental ideas related to classical Riemann solutions, ......
Riemann-Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann-Hilbert problem. This book, the most comprehensive one to date on the applied and ......
The book presents a solution to a problem in adaptive control design that was open for 40 years: robustification of disturbances without compromising asymptotic performance. This original methodology builds on foundational ideas, such as the use of a deadzone in the update law and nonlinear damping in the controller, and advances the tools for and ......
