Computational Techniques for the Summation of Series

Computational Techniques for the Summation of Series
Author: Anthony Sofo
Publisher: Springer Science & Business Media
Total Pages: 194
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461500575

"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

Methods for the Summation of Series

Methods for the Summation of Series
Author: Tian-Xiao He
Publisher: CRC Press
Total Pages: 301
Release: 2022-01-26
Genre: Mathematics
ISBN: 1000534375

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.

Computational Methods for Physicists

Computational Methods for Physicists
Author: Simon Sirca
Publisher: Springer Science & Business Media
Total Pages: 724
Release: 2012-12-17
Genre: Science
ISBN: 3642324789

This book helps 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 to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

Computational Methods for Inverse Problems

Computational Methods for Inverse Problems
Author: Curtis R. Vogel
Publisher: SIAM
Total Pages: 195
Release: 2002-01-01
Genre: Mathematics
ISBN: 0898717574

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Computational Methods in Physics

Computational Methods in Physics
Author: Simon Širca
Publisher: Springer
Total Pages: 894
Release: 2018-06-21
Genre: Science
ISBN: 3319786199

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.

Computational Methods for Nanoscale Applications

Computational Methods for Nanoscale Applications
Author: Igor Tsukerman
Publisher: Springer Science & Business Media
Total Pages: 543
Release: 2007-12-24
Genre: Technology & Engineering
ISBN: 0387747788

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.

Analytic Number Theory, Approximation Theory, and Special Functions

Analytic Number Theory, Approximation Theory, and Special Functions
Author: Gradimir V. Milovanović
Publisher: Springer
Total Pages: 873
Release: 2014-07-08
Genre: Mathematics
ISBN: 149390258X

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

High Performance Computational Methods for Biological Sequence Analysis

High Performance Computational Methods for Biological Sequence Analysis
Author: Tieng K. Yap
Publisher: Springer Science & Business Media
Total Pages: 219
Release: 2012-12-06
Genre: Computers
ISBN: 1461313910

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.

International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2004)

International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2004)
Author: Theodore Simos
Publisher: CRC Press
Total Pages: 1219
Release: 2019-04-29
Genre: Computers
ISBN: 1482284200

The International Conference of Computational Methods in Sciences and Engineering (ICCMSE) is unique in its kind. It regroups original contributions from all fields of the traditional Sciences, Mathematics, Physics, Chemistry, Biology, Medicine and all branches of Engineering. The aim of the conference is to bring together computational scientists from several disciplines in order to share methods and ideas. More than 370 extended abstracts have been submitted for consideration for presentation in ICCMSE 2004. From these, 289 extended abstracts have been selected after international peer review by at least two independent reviewers.