A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.
Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAEs) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of ......
This book is a guide to concepts and practice in numerical algebraic geometry - the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage ......
This book is about nonlinear observability. It provides a modern theory of observability based on a new paradigm borrowed from theoretical physics and the mathematical foundation of that paradigm. In the case of observability, this framework takes into account the group of invariance that is inherent to the concept of observability, allowing the ......
Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. ......
A Comprehensive Introduction to Modeling, Analysis, Simulation, Applications
Historically, optimal transport was about moving a pile of mortar efficiently or transferring the output of an array of steel mines optimally. This type of problem has been found to arise in many different fields of mathematics, science, and engineering-from fluid dynamics to many-electron physics to artificial intelligence-and in the last three ......
Mathematical Reviews said of this book that it was ""destined to become a classical reference"". It has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated ......
Developments in optimization theory, including emphasis on large problems and on interior-point methods for linear programming, have begun to appear in production software. Here is a reference tool that includes discussions of these areas and names software packages that incorporate the results of theoretical research. After an introduction to the ......
This work covers the fundamentals of the theory of ordinary differential equations (ODEs). It includes an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition, the text illustrates techniques involving simple topological arguments, fixed point theorems and basic facts of functional ......
