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Numerical Methods in Scientific Computing:
This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.
Introduction to High Performance Scientific Computing
Based on a course developed by the author, Introduction to High Performance Scientific Computing introduces methods for adding parallelism to numerical methods for solving differential equations. It contains exercises and programming projects that facilitate learning as well as examples and discussions based on the C programming language, with additional comments for those already familiar with C++. The text provides an overview of concepts and algorithmic techniques for modern scientific computing and is divided into six self-contained parts that can be assembled in any order to create an introductory course using available computer hardware. Part I introduces the C programming language for...
The Architecture of Scientific Software
Scientific applications involve very large computations that strain the resources of whatever computers are available. Such computations implement sophisticated mathematics, require deep scientific knowledge, depend on subtle interplay of different approximations, and may be subject to instabilities and sensitivity to external input. Software able to succeed in this domain invariably embeds significant domain knowledge that should be tapped for future use. Unfortunately, most existing scientific software is designed in an ad hoc way, resulting in monolithic codes understood by only a few developers. Software architecture refers to the way software is structured to promote objectives such as ...
The Art of Differentiating Computer Programs
This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as how to apply these observations to real-world numerical simulation programs. Readers will find: examples and exercises, including hints to solutions; the prototype AD tools dco and dcc for use with the examples and exercises; first- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc; a supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata.
Matrix Algebra
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Grid-Based Problem Solving Environments
This volume presents the proceedings of the IFIP TC2 WG 2.5 Conference on Grid-Based Problem Solving Environments: Implications for Development and Deployment of Numerical Software, held in Prescott, Arizona from July 17-21, 2006. The book contains the most up-to-date research on grid-based computing. It will interest users and developers of both grid-based and traditional problem solving environments, developers of grid infrastructure, and developers of numerical software.
Parallel MATLAB for Multicore and Multinode Computers
Parallel MATLAB for Multicore and Multinode Computers is the first book on parallel MATLAB and the first parallel computing book focused on the design, code, debug, and test techniques required to quickly produce well-performing parallel programs. MATLAB is currently the dominant language of technical computing with one million users worldwide, many of whom can benefit from the increased power offered by inexpensive multicore and multinode parallel computers. MATLAB is an ideal environment for learning about parallel computing, allowing the user to focus on parallel algorithms instead of the details of implementation. This book covers more parallel algorithms and parallel programming models than any other parallel programming book due to the succinctness of MATLAB and presents a "hands-on" approach with numerous example programs. Wherever possible, the examples are drawn from widely known and well-documented parallel benchmark codes representative of many real applications.
Mathematical Reviews
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Uncertainty Quantification in Scientific Computing
This book constitutes the refereed post-proceedings of the 10th IFIP WG 2.5 Working Conference on Uncertainty Quantification in Scientific Computing, WoCoUQ 2011, held in Boulder, CO, USA, in August 2011. The 24 revised papers were carefully reviewed and selected from numerous submissions. They are organized in the following topical sections: UQ need: risk, policy, and decision making, UQ theory, UQ tools, UQ practice, and hot topics. The papers are followed by the records of the discussions between the participants and the speaker.
