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Numerical Algorithms with C

Author: Giesela Engeln-Müllges
Publisher: Springer Science & Business Media
ISBN: 3642610749
Category : Mathematics
Languages : en
Pages : 597

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Book Description
More scientists now use C than any other programming language. This book contains practical, computer-ready algorithms for many standard methods of numerical mathematics. It describes the principles of the various methods and provides support in choosing the appropriate method for a given task. Topics given special emphasis include converging methods for solving nonlinear equations, methods for solving systems of linear equations for many special matrix structures, and the Shepard method for multidimensional interpolation. The CD contains C-programs for almost all the algorithms given in the book and a compiler, together with software for graphical printing.

Numerical Algorithms with C

Author: Giesela Engeln-Müllges
Publisher: Springer Science & Business Media
ISBN: 3642610749
Category : Mathematics
Languages : en
Pages : 597

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Numerical Algorithms

Author: Justin Solomon
Publisher: CRC Press
ISBN: 1482251892
Category : Computers
Languages : en
Pages : 400

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Book Description
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Parallel Numerical Algorithms

Author: David E. Keyes
Publisher: Springer Science & Business Media
ISBN: 9401154120
Category : Mathematics
Languages : en
Pages : 395

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Book Description
In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.

Accuracy and Stability of Numerical Algorithms

Author: Nicholas J. Higham
Publisher: SIAM
ISBN: 0898715210
Category : Mathematics
Languages : en
Pages : 680

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Book Description
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Control Perspectives on Numerical Algorithms and Matrix Problems

Author: Amit Bhaya
Publisher: SIAM
ISBN: 9780898718669
Category : Mathematics
Languages : en
Pages : 297

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Book Description
Control Perspectives on Numerical Algorithms and Matrix Problems organizes the analysis and design of iterative numerical methods from a control perspective. The authors discuss a variety of applications, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems, support vector machines, integration and shooting methods for ordinary differential equations, matrix preconditioning, matrix stability, and polynomial zero finding. This book opens up a new field of interdisciplinary research that should lead to insights in the areas of both control and numerical analysis and shows that a wide range of applications can be approached from, and benefit from, a control perspective.

Structure-Exploiting Numerical Algorithms for Optimal Control

Author: Isak Nielsen
Publisher: Linköping University Electronic Press
ISBN: 9176855287
Category :
Languages : en
Pages : 179

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Book Description
Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.

Variational Methods

Author: John M. Neuberger
Publisher: American Mathematical Soc.
ISBN: 0821833391
Category : Mathematics
Languages : en
Pages : 285

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Book Description
A conference was organized to discuss research in variational methods as applied to nonlinear elliptic PDE. This volume resulted from that gathering. Included in this title are both survey and research papers that address important open questions and offer suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.

Practical Numerical Algorithms for Chaotic Systems

Author: Thomas S. Parker
Publisher: Springer Science & Business Media
ISBN: 1461234867
Category : Science
Languages : en
Pages : 348

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Book Description
One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.

The Developments and the Applications of the Numerical Algorithms in Simulating the Incompressible Magnetohydrodynamics with Complex Boundaries and Free Surfaces

Author: Jie Zhang
Publisher: Springer
ISBN: 9811063400
Category : Technology & Engineering
Languages : en
Pages : 145

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Book Description
This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble’s path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.

Numerical Algorithms for Personalized Search in Self-organizing Information Networks

Author: Sep Kamvar
Publisher: Princeton University Press
ISBN: 1400837065
Category : Computers
Languages : en
Pages : 160

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Book Description
This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data. Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quadratic extrapolation technique--that speed up computation, making personalized PageRank feasible. Kamvar suggests that Power Method-related techniques ultimately should be the basis for improving the PageRank algorithm, and he presents algorithms that exploit the convergence behavior of individual components of the PageRank vector. Kamvar then extends the ideas of reputation management and personalized search to distributed networks like peer-to-peer and social networks. He highlights locality and computational considerations related to the structure of the network, and considers such unique issues as malicious peers. He describes the EigenTrust algorithm and applies various PageRank concepts to P2P settings. Discussion chapters summarizing results conclude the book's two main sections. Clear and thorough, this book provides an authoritative look at central innovations in search for all of those interested in the subject.