Computational Techniques for the Summation of Series

Author: Anthony Sofo
Publisher: Springer Science & Business Media
ISBN: 1461500575
Format: PDF, Docs
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"This book collects in one volume the author’s considerable results in the area of the summation of series and their representation in closed form, and details the techniques by which they have been obtained... the calculations are given in plenty of detail, and closely related work which has appeared in a variety of places is conveniently collected together." --The Australian Mathematical Society Gazette

Computational Methods in Physics

Author: Simon Širca
Publisher: Springer
ISBN: 3319786199
Format: PDF, ePub, Docs
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This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

Integral Representation and the Computation of Combinatorial Sums

Author: G. P. Egorychev
Publisher: American Mathematical Soc.
ISBN: 9780821898093
Format: PDF
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This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.

Computational Methods for Nanoscale Applications

Author: Igor Tsukerman
Publisher: Springer Science & Business Media
ISBN: 9780387747781
Format: PDF
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Positioning itself at the common boundaries of several disciplines, this work provides new perspectives on modern nanoscale problems where fundamental science meets technology and computer modeling. In addition to well-known computational techniques such as finite-difference schemes and Ewald summation, the book presents a new finite-difference calculus of Flexible Local Approximation Methods (FLAME) that qualitatively improves the numerical accuracy in a variety of problems.

High Performance Computational Methods for Biological Sequence Analysis

Author: Tieng K. Yap
Publisher: Springer Science & Business Media
ISBN: 1461313910
Format: PDF, Mobi
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High Performance Computational Methods for Biological Sequence Analysis presents biological sequence analysis using an interdisciplinary approach that integrates biological, mathematical and computational concepts. These concepts are presented so that computer scientists and biomedical scientists can obtain the necessary background for developing better algorithms and applying parallel computational methods. This book will enable both groups to develop the depth of knowledge needed to work in this interdisciplinary field. This work focuses on high performance computational approaches that are used to perform computationally intensive biological sequence analysis tasks: pairwise sequence comparison, multiple sequence alignment, and sequence similarity searching in large databases. These computational methods are becoming increasingly important to the molecular biology community allowing researchers to explore the increasingly large amounts of sequence data generated by the Human Genome Project and other related biological projects. The approaches presented by the authors are state-of-the-art and show how to reduce analysis times significantly, sometimes from days to minutes. High Performance Computational Methods for Biological Sequence Analysis is tremendously important to biomedical science students and researchers who are interested in applying sequence analyses to their studies, and to computational science students and researchers who are interested in applying new computational approaches to biological sequence analyses.

Computational Methods in Chemical Engineering

Author: Owen T. Hanna
Publisher: Prentice Hall
ISBN: 9780133073980
Format: PDF, Mobi
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Presenting a clear, concise exposition of practical computational methods in chemical engineering, this book provides a bridge between introductory applications and more advanced levels of mathematics. Authors Owen Hanna and Orville Sandall include broad use of convergence acceleration techniques such as Pade approximation for series; Shanks transformation for series; linear and nonlinear systems of algebraic equations; systematic use of global Richardson extrapolation for integrals and ODE systems to monitor the overall error; and discussion of methods for the solution of stiff ODE. In addition, some 25 user-friendly microcomputer programs which are demonstrated and used for many of the problems are available in IBM format on the accompanying diskette in FORTRAN 77 and True BASIC.

Integral Methods in Science and Engineering

Author: Christian Constanda
Publisher: CRC Press
ISBN: 9780582304093
Format: PDF
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These conference proceedings are concerned with the solution of mathematical models from various physical domains, by means of integral methods in conjunction with various approximation schemes.

Artificial Intelligence Expert Systems Symbolic Computing

Author: E.N. Houstis
Publisher: Elsevier
ISBN: 044459888X
Format: PDF, Mobi
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This volume contains papers in the areas of artificial intelligence, expert systems, symbolic computing and applications to scientific computing. Together, they provide an excellent overview of the dynamic state of these closely related fields. They reveal a future where scientific computation will increasingly involve symbolic and artificial intelligence tools as these software systems become more sophisticated; also a future where systems of computational science and engineering will be problem solving environments created with components from numerical analysis, computational geometry, symbolic computing and artificial intelligence.

Mathematical and Computational Techniques for Multilevel Adaptive Methods

Author: Ulrich R?de
Publisher: SIAM
ISBN: 9781611970968
Format: PDF, ePub, Docs
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Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures. Rüde introduces a well-founded mathematical theory that leads to intelligent, adaptive algorithms, and suggests advanced software techniques. This new kind of multigrid theory supports the so-called "BPX" and "multilevel Schwarz" methods, and leads to the discovery of faster more robust algorithms. These techniques are deeply rooted in the theory of function spaces. Mathematical and Computational Techniques for Multilevel Adaptive Methods examines this development together with its implications for relevant algorithms for adaptive PDE methods. The author shows how abstract data types and object-oriented programming can be used for improved implementation.