A Course in Approximation Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 101)

this Textbook Is Designed For Graduate Students In Mathematics, Physics, Engineering, And Computer Science. Its Purpose Is To Guide The Reader In Exploring Contemporary Approximation Theory. The Emphasis Is On Multi-variable Approximation Theory, I.e., The Approximation Of Functions In Several Variables, As Opposed To The Classical Theory Of Functions In One Variable. Most Of The Topics In The Book, Heretofore Accessible Only Through Research Papers, Are Treated Here From The Basics To The Currently Active Research, Often Motivated By Practical Problems Arising In Diverse Applications Such As Science, Engineering, Geophysics, And Business And Economics. Among These Topics Are Projections, Interpolation Paradigms, Positive Definite Functions, Interpolation Theorems Of Schoenberg And Micchelli, Tomography, Artificial Neural Networks, Wavelets, Thin-plate Splines, Box Splines, Ridge Functions, And Convolutions. An Important And Valuable Feature Of The Book Is The Bibliography Of Almost 600 Items Directing The Reader To Important Books And Research Papers. There Are 438 Problems And Exercises Scattered Through The Book Allowing The Student Reader To Get A Better Understanding Of The Subject. booknews the Central Theme Of The Graduate Textbook Is The Problem Of Interpolating Data By Smooth Multivariable Functions. Several Chapters Investigate Interesting Families Of Functions That Can Be Employed In This Task. The Book Then Moves On To The Consideration Of Methods For Concocting Approximations, Such As By Convolutions, By Neural Nets, Or By Interpolation At More And More Points. Annotation C. Book News, Inc., Portland, Or (booknews.com) "This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable." "An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject."--Jacket Suitable for students in mathematics, physics, engineering, and computer science, this book explores contemporary approximation theory. It covers such topics as projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, and thin-plate splines.