[PDF] Divided Differences Falling Factorials And Discrete Splines eBook

Author : Ryan J. Tibshirani
Publisher :
Page : 0 pages
File Size : 10,75 MB
Release : 2022
Category : COMPUTERS
ISBN : 9781638280378

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This monograph reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by continuity in divided differences. As it happens, discrete splines bear connections to a wide array of developments in applied mathematics and statistics, from divided differences and Newton interpolation, dating back 300 years, to the recent emergence of trend filtering. In this concise yet comprehensive monograph, the author uses his recognized expertise on the subject to guide the reader through these connections. In doing so, the author provides an insightful journey through the historical and most recent developments, contributing some new perspectives and results along the way.Written for researchers and advanced level students of applied mathematics and statistics, this monograph will be of particular interest to those using trend filtering in machine learning applications.

Author : Ryan J. Tibshirani
Publisher :
Page : 0 pages
File Size : 21,64 MB
Release : 2022-07-21
Category : Machine learning
ISBN : 9781638280361

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This monograph reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by continuity in divided differences. As it happens, discrete splines bear connections to a wide array of developments in applied mathematics and statistics, from divided differences and Newton interpolation, dating back 300 years, to the recent emergence of trend filtering. In this concise yet comprehensive monograph, the author uses his recognized expertise on the subject to guide the reader through these connections. In doing so, the author provides an insightful journey through the historical and most recent developments, contributing some new perspectives and results along the way. Written for researchers and advanced level students of applied mathematics and statistics, this monograph will be of particular interest to those using trend filtering in machine learning applications.

Author : Denis Belomestny
Publisher : Springer Nature
Page : 603 pages
File Size : 14,21 MB
Release : 2023-07-16
Category : Mathematics
ISBN : 3031301145

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This book contains contributions from the participants of the international conference “Foundations of Modern Statistics” which took place at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, during November 6–8, 2019, and at Higher School of Economics (HSE University), Moscow, during November 30, 2019. The events were organized in honor of Professor Vladimir Spokoiny on the occasion of his 60th birthday. Vladimir Spokoiny has pioneered the field of adaptive statistical inference and contributed to a variety of its applications. His more than 30 years of research in the field of mathematical statistics had a great influence on the development of the mathematical theory of statistics to its present state. It has inspired many young researchers to start their research in this exciting field of mathematics. The papers contained in this book reflect the broad field of interests of Vladimir Spokoiny: optimal rates and non-asymptotic bounds in nonparametrics, Bayes approaches from a frequentist point of view, optimization, signal processing, and statistical theory motivated by models in applied fields. Materials prepared by famous scientists contain original scientific results, which makes the publication valuable for researchers working in these fields. The book concludes by a conversation of Vladimir Spokoiny with Markus Reiβ and Enno Mammen. This interview gives some background on the life of Vladimir Spokoiny and his many scientific interests and motivations.

Author : Annette M. Bolden
Publisher :
Page : 74 pages
File Size : 38,55 MB
Release : 1998
Category : Divided differences
ISBN :

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"The main objective of this thesis project is to apply the definition of divided difference to polynomial splines. We begin by introducing different definitions of divided differences and proving their equivalence. Another main objective is to establish explicit formulas for divided differences with pairwisely distinct knots and confluent or repeated knots."--(v).

Author : William H. Press
Publisher :
Page : 0 pages
File Size : 27,92 MB
Release : 2002
Category : Computers
ISBN : 9788175960961

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Now the acclaimed Second Edition of Numerical Recipes is available in the C++ object-oriented programming language. Including and updating the full mathematical and explanatory contents of Numerical Recipes in C, this new version incorporates completely new C++ versions of the more than 300 Numerical Recipes routines that are widely recognized as the most accessible and practical basis for scientific computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. Highlights include linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations and inverse theory. The authors approach to C++ preserves the efficient execution that C users expect, while simultaneously employing a clear, object-oriented interface to the routines. Tricks and tips for scientific computing in C++ are liberally included. The routines, in ANSI/ISO C++ source code, can thus be used with almost any existing C++ vector/matrix class library, according to user preference. A simple class library for stand-alone use is also included in the book. Both scientific programmers new to C++, and experienced C++ programmers who need access to the Numerical Recipes routines, can benefit from this important new version of an invaluable, classic text.

Author : G. Jay Kerns
Publisher : Lulu.com
Page : 388 pages
File Size : 43,77 MB
Release : 2010-01-10
Category : Education
ISBN : 0557249791

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This is a textbook for an undergraduate course in probability and statistics. The approximate prerequisites are two or three semesters of calculus and some linear algebra. Students attending the class include mathematics, engineering, and computer science majors.

Author : József Sándor
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 21,49 MB
Release : 2005-11-17
Category : Mathematics
ISBN : 1402042159

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This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Author : William H. Press
Publisher : Cambridge University Press
Page : 0 pages
File Size : 33,81 MB
Release : 1992-09-25
Category : Mathematics
ISBN : 9780521430647

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This is the greatly revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, this new edition remains the most practical, comprehensive handbook of scientific computing available today. Highlights of the new material include: -A new chapter on integral equations and inverse methods -Multigrid and other methods for solving partial differential equations -Improved random number routines - Wavelet transforms -The statistical bootstrap method -A new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic. The book retains the informal easy-to-read style that made the first edition so popular, while introducing some more advanced topics. It is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. The Second Edition is availabe in FORTRAN, the traditional language for numerical calculations and in the increasingly popular C language.

Author : Gary W. Oehlert
Publisher : W. H. Freeman
Page : 600 pages
File Size : 50,68 MB
Release : 2000-01-19
Category : Mathematics
ISBN : 9780716735106

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Oehlert's text is suitable for either a service course for non-statistics graduate students or for statistics majors. Unlike most texts for the one-term grad/upper level course on experimental design, Oehlert's new book offers a superb balance of both analysis and design, presenting three practical themes to students: • when to use various designs • how to analyze the results • how to recognize various design options Also, unlike other older texts, the book is fully oriented toward the use of statistical software in analyzing experiments.