On May 1, 2004, the world of theoretical computer science su?ered a stunning loss: Shimon Even passed away. Few computer scientists have had as long, s- tained, and in?uential a career as Shimon. Shimon Even was born in Tel-Aviv in 1935. He received a B.Sc. in Elect- cal Engineering from the Technion in 1959, an M.A. in Mathematics from the University of Northern Carolina in 1961, and a Ph.D. in Applied Mathematics from Harvard University in 1963. He held positions at the Technion (1964–67 and 1974–2003), Harvard University (1967–69), the Weizmann Institute (1969– 74), and the Tel-Aviv Academic College (2003-04). He visited many universities and research institutes, including Bell Laboratories, Boston University, Cornell, Duke, Lucent Technologies, MIT, Paderborn, Stanford, UC-Berkeley, USC and UT-Dallas. Shimon Even played a major role in establishing computer science education in Israel and led the development of academic programs in two major insti- tions: the Weizmann Institute and the Technion. In 1969 he established at the Weizmann the ?rst computer science education program in Israel, and led this program for ?ve years. In 1974 he joined the newly formed computer science department at the Technion and shaped its academic development for several decades. These two academic programs turned out to have a lasting impact on the evolution of computer science in Israel.

The numerical optimization of practical applications is an issue of growing importance in research and industry. It allows both the exploration of non-trivial configurations differing widely from all known solutions and the step-by-step improvement of existing designs.

This book is meant as a present to honor Professor on the th occasion of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from eleven countries. They cover many different areas of research related to the work of Professor including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions of parabolic and elliptic problems, operator theory and numerical methods. The realization of this book could not have been made possible without the generous support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. Special thanks are due to Dr. Ulrych for the careful preparation of the final version of this book. Last but not least, we wish to express our gratitude to Dr. for her invaluable assistance from the very beginning. This project could not have been successfully concluded without her enthusiasm and loving care for her father. On behalf of the editors ADÉLIA SEQUEIRA v honored by the Order of Meritof the Czech Republic by Václav Havel, President of the Czech Republic, on the October 28, 1998, Professor Emeritus of Mathematics at the Charles University in Prague, Presidential Research Professor at the Northern Illinois University and Doctor Honoris Causa at the Technical University of Dresden, has been enriching the Czech and world mathematics with his new ideas in the areas of partial differential equations, nonlinear functional analysis and applications of the both disciplines in continuum mechanics and hydrodynamics for more than forty years.

This book describes the rapidly developing field of interior point methods (IPMs). An extensive analysis is given of path-following methods for linear programming, quadratic programming and convex programming. These methods, which form a subclass of interior point methods, follow the central path, which is an analytic curve defined by the problem. Relatively simple and elegant proofs for polynomiality are given. The theory is illustrated using several explicit examples. Moreover, an overview of other classes of IPMs is given. It is shown that all these methods rely on the same notion as the path-following methods: all these methods use the central path implicitly or explicitly as a reference path to go to the optimum.

In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.

In the last decade, we have seen an extraordinary progress in the the­ ory and applications of robot kinematics. This has been motivated espe­ cially by the development of complex parallel and humanoid robots. The present book reports the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automa­ tion, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, re­ dundancy, force control, dexterity, inverse and forward kinematics, kine­ matic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw algebra, and linear alge­ bra. These methods are applied to both parallel and serial multi-degree­ of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathematics related to robot theory, design, control and application. This is the sixth book of the series Advances in Robot Kinematics published by Kluwer. The contributions in this book had been rigorously reviewed by in­ dependent reviewers and fifty one articles had been recommended for publication. They were introduced in seven chapters. These articles were also reported and discussed at the ninth international symposium on Advances in Robot Kinematics which was held in June 2004 in Sestri Levante in Italy.

The book introduces the key ideas behind practical nonlinear optimization. Computational finance – an increasingly popular area of mathematics degree programs – is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material – which occupies about one-third of the text – is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performance is demonstrated on a range of optimization problems arising in financial mathematics. Theoretical convergence properties of methods are stated, and formal proofs are provided in enough cases to be instructive rather than overwhelming. Practical behavior of methods is illustrated by computational examples and discussions of efficiency, accuracy and computational costs. Supporting software for the examples and exercises is available (but the text does not require the reader to use or understand these particular codes). The author has been active in optimization for over thirty years in algorithm development and application and in teaching and research supervision.

Despite the ample number of articles on parallel-vector computational algorithms published over the last 20 years, there is a lack of texts in the field customized for senior undergraduate and graduate engineering research. Parallel-Vector Equation Solvers for Finite Element Engineering Applications aims to fill this gap, detailing both the theoretical development and important implementations of equation-solution algorithms. The mathematical background necessary to understand their inception balances well with descriptions of their practical uses. Illustrated with a number of state-of-the-art FORTRAN codes developed as examples for the book, Dr. Nguyen's text is a perfect choice for instructors and researchers alike.

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover­ ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag­ netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys­ tems, communication theory, mathematical economics, population genetics, queue­ ing theory, and medicine. Most of the boundary value problems involving differ­ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

This is the fifth book of the Kluwer's series Advances in Robot Kine­ matics. The book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufactur­ ing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw alge­ bra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathe­ matics related to robot theory, design, control and application. Each contribution in this book had been rigorously reviewed by two or three independent reviewers and 53 articles had been recommended for publication. We are happy to observe that Advances in Robot Kine­ matics has always attracted the most outstanding authors and has de­ veloped a remarkable scientific community in the area. Many important and original scientific results were for the first time reported and dis­ cussed in these books. All articles in this book were also reported at the eight international symposium on Advances in Robot Kinematics that was organised in June 2002 in Caldes de Malavella in Spain.

This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci­ sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer­ ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu­ able comments. Special thanks are directed to our sponsors, the Hun­ garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor­ rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.

In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new the new vistas edition of this textbook must therefore take into account some of that have opened up recently. Apart from these additions and some didactic improvements, the general struc­ ture of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics. I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site www.ap.univie.ac.at/users/Franz.Vesely/ to see if any new applets have sprung up.

Th e variational spline theory which originates f rom th e well-known paper by J.e. Holliday (1957) is today a well-developed field in approxi- mat ion theory. The gene ra l definition of splines in the Hilbert space, ex- istence, uniqueness, and characterization theorems were obt ained about 35 years ago by M. Atteia, P.J. L aur ent, and P.M. Anselone, but in rec ent years impor tant new results have been obtained in th e abst ract variational spline theory. Th ese concern the convergence in th e Hilb ert spaces, general techniques for error es tim ation of abs trac t splines includ- ing multi-dimensional splines on scatt ered meshes, new kinds of charac- teriz ation th eorems based on reproducing kernels and m appin gs, and the theory and algorithms for the splines on subspaces (finite element me th od for complic at ed non-polynomial splines). New variatio na l for- mulations arose for vec tor splines, rational splines, te nsor and blending splines, trac es of splines on the smooth manifold, discontinuous splines, etc. Optim al approxi mat ions of linear functionals and ope rat ors are also developed from th ese concepts.

This book is intended to be an easy, concise, but rather complete, introduc­ the ISO/ANSI C++ programming language with special empha­ tion to sis on object-oriented numeric computation for students and professionals in science and engineering. The description of the language is platform­ independent. Thus it applies to different operating systems such as UNIX, Linux, MacOS, Windows, and DOS, as long as a standard C++ compiler is equipped. The prerequisite of this book is elementary knowledge of cal­ culus and linear algebra. However, this prerequisite is hardly necessary if this book is going to be used as a textbook for teaching C++ and all the sections on numeric methods are skipped. Programming experience in an­ other language such as FORTRAN, C, Ada, Pascal, Maple, or Matlab will certainly help, but is not presumed. All C++ features are introduced in an easy way through concepts such as functions, complex numbers, vectors, matrices, and integrals, which are familiar to every student and professional in science and engineering.

Deals with the most basic notion of linear algebra, to bring emphasis on approaches to the topic serving at the elementary level and more broadly.