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 ......
This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author's decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines ......
Collecting a set of classical and emerging methods that otherwise would not be available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book is designed to bring together an eclectic ......
Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent ......
In 1940 G. H. Hardy published A Mathematician's Apology, a meditation on mathematics by a leading pure mathematician. Eighty-two years later, An Applied Mathematician's Apology is a meditation and also a personal memoir by a philosophically inclined numerical analyst, one who has found great joy in his work but is puzzled by its relationship to ......
This innovative book introduces finite and transfinite interpolation methods at a general level in a unifying mathematical style before covering dynamical interpolation methods, which emphasize the underlying Eulerian/Lagrangian dynamics. Transfinite Interpolations and Eulerian/Lagrangian Dynamics: Considers the support of the data set as a ......
Building on the authors' many years of experience running creativity workshops, How to Be Creative: A Practical Guide for the Mathematical Sciences: Gives a six-step process for generating great ideas that can be used by individuals or groups. Provides examples demonstrating how these concepts have been or might be used in practice in the ......
Fit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems. Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond ......
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 ......
