Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods.The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
In The Invertebrate Tree of Life, Gonzalo Giribet and Gregory Edgecombe, leading authorities on invertebrate biology and paleontology, utilize phylogenetics to trace the evolution of animals from their origins in the Proterozoic to today. Phylogenetic relationships between and within the major animal groups are based on the latest molecular analyses, which are increasingly genomic in scale and draw on the soundest methods of tree reconstruction. Giribet and Edgecombe evaluate the evolution of animal organ systems, exploring how current debates about phylogenetic relationships affect the ways in which aspects of invertebrate nervous systems, reproductive biology, and other key features are inferred to have developed. The authors review the systematics, natural history, anatomy, development, and fossil records of all major animal groups, employing seminal historical works and cutting-edge research in evolutionary developmental biology, genomics, and advanced imaging techniques. Overall, they provide a synthetic treatment of all animal phyla and discuss their relationships via an integrative approach to invertebrate systematics, anatomy, paleontology, and genomics. With numerous detailed illustrations and phylogenetic trees, The Invertebrate Tree of Life is a must-have reference for biologists and anyone interested in invertebrates, and will be an ideal text for courses in invertebrate biology. A must-have and up-to-date book on invertebrate biology Ideal as both a textbook and reference Suitable for courses in invertebrate biology Richly illustrated with black-and-white and color images and abundant tree diagrams Written by authorities on invertebrate evolution and phylogeny Factors in the latest understanding of animal genomics and original fossil material" --Amazon.com.
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