Author : Petr Kurka
Publisher : Springer
Page : 229 pages
File Size : 31,56 MB
Release : 2016-06-01
Category : Technology & Engineering
ISBN : 3319333674
This book is a source of valuable and useful information on the topics of dynamics of number systems and scientific computation with arbitrary precision. It is addressed to scholars, scientists and engineers, and graduate students. The treatment is elementary and self-contained with relevance both for theory and applications. The basic prerequisite of the book is linear algebra and matrix calculus.
Author : Dzmitry Badziahin
Publisher : Cambridge University Press
Page : 341 pages
File Size : 39,65 MB
Release : 2016-11-10
Category : Mathematics
ISBN : 1107552370
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
Author : Ghada Alsuhli
Publisher : Springer Nature
Page : 100 pages
File Size : 25,48 MB
Release : 2023-09-01
Category : Technology & Engineering
ISBN : 3031381335
This book provides readers a comprehensive introduction to alternative number systems for more efficient representations of Deep Neural Network (DNN) data. Various number systems (conventional/unconventional) exploited for DNNs are discussed, including Floating Point (FP), Fixed Point (FXP), Logarithmic Number System (LNS), Residue Number System (RNS), Block Floating Point Number System (BFP), Dynamic Fixed-Point Number System (DFXP) and Posit Number System (PNS). The authors explore the impact of these number systems on the performance and hardware design of DNNs, highlighting the challenges associated with each number system and various solutions that are proposed for addressing them.
Author : Amos R. Omondi
Publisher : Imperial College Press
Page : 311 pages
File Size : 47,59 MB
Release : 2007
Category : Technology & Engineering
ISBN : 1860948677
Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today. This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.
Author : P.V. Ananda Mohan
Publisher : Birkhäuser
Page : 353 pages
File Size : 43,72 MB
Release : 2016-10-14
Category : Mathematics
ISBN : 3319413856
This new and expanded monograph improves upon Mohan's earlier book, Residue Number Systems (Springer, 2002) with a state of the art treatment of the subject. Replete with detailed illustrations and helpful examples, this book covers a host of cutting edge topics such as the core function, the quotient function, new Chinese Remainder theorems, and large integer operations. It also features many significant applications to practical communication systems and cryptography such as FIR filters and elliptic curve cryptography. Starting with a comprehensive introduction to the basics and leading up to current research trends that are not yet widely distributed in other publications, this book will be of interest to both researchers and students alike.
Author : Stephen Chrisomalis
Publisher : MIT Press
Page : 265 pages
File Size : 22,64 MB
Release : 2020-12-15
Category : Mathematics
ISBN : 026236087X
Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation--distinct ways of writing numbers--have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words.
Author : Claus Führer
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 34,6 MB
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 3663098281
The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck thoughout the book to illustrate all key concepts.
Author : Yaneer Bar-yam
Publisher : CRC Press
Page : 866 pages
File Size : 29,27 MB
Release : 2019-03-04
Category : Mathematics
ISBN : 0429717598
This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.
Author : Valérie Berthé
Publisher : Birkhäuser
Page : 591 pages
File Size : 27,23 MB
Release : 2018-04-09
Category : Mathematics
ISBN : 331969152X
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Author : S.T. Zavalishchin
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 26,81 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 9401588937
A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco momics and biology, have an irregular structure: classical variational proce dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.
