Globally Convergent Homotopy Methods A Tutorial
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Introduction to Numerical Continuation Methods
| Author | : Eugene L. Allgower |
| Publisher | : SIAM |
| Total Pages | : 409 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871544X |
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.
Numerical Continuation Methods
| Author | : Eugene L. Allgower |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642612571 |
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Circuit Simulation Methods and Algorithms
| Author | : Jan Ogrodzki |
| Publisher | : CRC Press |
| Total Pages | : 490 |
| Release | : 2018-05-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1351460633 |
Circuit Simulation Methods and Algorithms provides a step-by-step theoretical consideration of methods, techniques, and algorithms in an easy-to-understand format. Many illustrations explain more difficult problems and present instructive circuits. The book works on three levels: The simulator-user level for practitioners and students who want to better understand circuit simulators. The basic theoretical level, with examples, dedicated to students and beginning researchers. The thorough level for deep insight into circuit simulation based on computer experiments using PSPICE and OPTIMA. Only basic mathematical knowledge, such as matrix algebra, derivatives, and integrals, is presumed.
Supercomputing in Engineering Analysis
| Author | : Hojjat Adeli |
| Publisher | : CRC Press |
| Total Pages | : 377 |
| Release | : 2020-08-13 |
| Genre | : Computers |
| ISBN | : 1000104680 |
The first volume in this new series has a companion in volume 2 (unseen), Parallel processing in computational mechanics . The first six contributions present general aspects of supercomputing from both hardware and software engineering points of view. Subsequent chapters discuss homotopy algorithms
Solving Polynomial Equations
| Author | : Alicia Dickenstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2005-12-29 |
| Genre | : Mathematics |
| ISBN | : 3540273573 |
The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.
Advances in Optimization and Numerical Analysis
| Author | : S. Gomez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401583307 |
In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.
Homotopy Methods and Global Convergence
| Author | : B. Curtis Eaves |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 319 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461335728 |
This Proceedings presents refereed versions of most of the papers presented at the NATO Advanced Research Institute on Homotopy Methods and Global Convergence held in Porto Cervo, Sardinia, June 3-6, 1981. This represents the fourth recent occurrence of an international conference addressing the common theme of fixed point computation. The first such conference, ti tled "Computing Fixed Points with Applications," was held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina, June 26-28, 1974 and was sponsored by the Office of Naval Research and the Office of the Army Research Center. The second conference, "Symposium on Analysis and Computation of Fixed Points," was held at the University of Wisconsin, Madison, May 7-8, 1979, under the sponsorship of the National Science Foundation, the U. S. Army, and the Mathematics Research Center of the University of Wisconsin, Madison. The third conference, titled "Symposium on Fixed Point Algorithms and Complementarity," was held at the University of Southampton, Southampton, UK, July 3-5, 1979 and was sponsored by U. N. E. S. C. O. , European Research Office (London), Department of Mathematics (University of Southampton), I. B. M. U. K. , Ltd. , Lloyds Bank, Ltd. , and the Office of Naval Research (London). The Advanced Research Institute held in Sardinia was devoted to the theory and application of modern homotopy methods. The following topics were stressed: Path-Following Techniques; Bottom-Line Applications; Global vs. Classical Methods; and Sta- v vi PREFACE of-the-Art, Perspectives and Potential.
Nonlinear Optimization and Applications
| Author | : Gianni Pillo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2013-11-11 |
| Genre | : Computers |
| ISBN | : 1489902899 |
This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization prob lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the partici pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume.
Boundary Value Problems for Engineers
| Author | : Ali Ümit Keskin |
| Publisher | : Springer |
| Total Pages | : 523 |
| Release | : 2019-06-19 |
| Genre | : Technology & Engineering |
| ISBN | : 3030210804 |
This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).
