Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers....

This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at...

We are surrounded by data, numerical and otherwise, which must be analyzed and processed to convert it into information that informs, instructs, answers, or otherwise aids understanding and decision-making. Due to the ever-increasing complexity and size of today’s data sets, a new term, data mining, was created to describe the...

Since the advent of computerized tomography in radiology, many imaging techniques have been introduced in medicine, science, and technology. This book describes the state of the art of the mathematical theory and numerical analysis of imaging. The authors survey and provide a unified view of imaging techniques, provide the necessary...

Dynamics of Ice Sheets and Glaciers presents an introduction to the dynamics and thermodynamics of flowing ice masses on Earth. Based on an outline of general continuum mechanics, the different initial-boundary-value problems for the flow of ice sheets, ice shelves, ice caps and glaciers are systematically derived. Special emphasis is put on...

The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating...

The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of...

This text began as notes for a course in statistical computing for second year actuarial and statistical students at the University of Western Ontario. Both authors are interested in statistical computing, both as support for our other research and for its own sake. However, we have found that our students were not learning the right sort of...