The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.

This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.

Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.

Though the volume covers 22 papers by 36 authors from 12 countries, the history in the background is bound to Hungary where, in 1973 Andras Pn§kopa started to lay the foundation of a scientific forum, which can be a regular meeting spot for experts of the world in the field. Since then, there has been a constant interest in that forum. Headed at present by Tamas Rapcsak, the Laboratory of Operations Research and Decisions Systems of the Computer and Automation Institute, Hungarian Academy of Sciences followed the tradition in every respect, namely conferences were organized almost in every second year and in the same stimulating area, in the Matra mountains. The basic fields were kept, providing opportunities for the leading personalities to give voice to their latest results. The floor has been widened recently for the young generation, ensuring this way both a real location for the past, present and future experts to meet and also the possibility for them to make the multicoloured rainbow of the fields unbroken and continuous. The volume is devoted to the memory of Steven Vajda, one of the pioneers on mathematical programming, born is Hungary. In 1992 he took part in the XIth International Conference on Mathematical Programming at Matrafiired where, with his bright personality, he greatly contributed to the good spirituality of the event. We thank Jakob Krarup for his reminiscence on the life and scientific activities of late Steven Vajda.

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.

In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.