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 ......
Applied Numerical Linear Algebra introduces students to numerical issues that arise in linear algebra and its applications. A wide range of techniques are touched on, including direct to iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Inside Applied Numerical Linear Algebra, readers will find: ......
Starting with the fundamentals of classical smooth optimization and building on established convex programming techniques, this research monograph presents a foundation and methodology for modern nonconvex nondifferentiable optimization. It provides readers with theory, methods, and applications of nonconvex and nondifferentiable optimization in ......
Iterative methods use successive approximations to obtain more accurate solutions. Iterative Methods and Preconditioners for Systems of Linear Equations presents historical background, derives complete convergence estimates for all methods, illustrates and provides Matlab codes for all methods, and studies and tests all preconditioners first as ......
Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and iterative methods for solving systems of linear equations. Systematic methods and rigorous theory on ......
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 problems and is divided into two parts: Part I covers ......
