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Introduction to Numerical Continuation Methods
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.
Nonlinear Equations and Optimisation
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work co...
Numerical Methods for Bifurcations of Dynamical Equilibria
Numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems.
Mechanics and Control
The Workshop on Control Mechanics has been held at the University of South ern California annually since 1988 under the leadership of late Professor Janislaw M. Skowronski. The primary goal of Professor Skowronski in organizing this series of work shops was to promote the use of advanced mechanics method in control theory with a special emphasis on the control of nonlinear mechanical systems subject to uncertainty. This goal has been achieved through a consistent participation of a large number of researchers in the field of control and mechanics and an intensive exchange of their ideas. Professor Skowronski passed away unexpectedly on March 21, 1992, after the conclusion of the Fifth Worksh...
Solving Polynomial Equations
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Interactions of Classical and Numerical Algebraic Geometry
This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.
Advances in Scientific Visualization
Scientific visualization is a new and rapidly growing area in which efforts from computer graphics research and many scientific and engineering disciplines are integrated. Its aim is to enhance interpretation and understanding by scientists of large amounts of data from measurements or complex computer simulations, using computer generated images and animation sequences. It exploits the power of human visual perception to identify trends and structures, and recognize shapes and patterns. Development of new numerical simulation methods in many areas increasingly depends on visualization as an effective way to obtain an intuitive understanding of a problem. This book contains a selection of pa...
Generalized Inverses
This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
Intelligent Information Processing II
Data Mining is the process of posing queries and extracting useful information, patterns and trends previously unknown from large quantities of data [Thu, 00]. It is the process where intelligent tools are applied in order to extract data patterns [JM, 01]. This encompasses a number of different technical approaches, such as cluster analysis, learning classification and association rules, and finding dependencies. Agents are defined as software entities that perform some set of tasks on behalf of users with some degree of autonomy. This research work deals about developing a automated data mining system which encompasses the familiar data mining algorithms using intelligent agents in object ...
Newton Methods for Nonlinear Problems
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
