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This book provides a friendly introduction to the paradigm and
proposes a broad panorama of killing applications of the Infinity
Computer in optimization: radically new numerical algorithms, great
theoretical insights, efficient software implementations, and
interesting practical case studies. This is the first book
presenting to the readers interested in optimization the advantages
of a recently introduced supercomputing paradigm that allows to
numerically work with different infinities and infinitesimals on
the Infinity Computer patented in several countries. One of the
editors of the book is the creator of the Infinity Computer, and
another editor was the first who has started to use it in
optimization. Their results were awarded by numerous scientific
prizes. This engaging book opens new horizons for researchers,
engineers, professors, and students with interests in
supercomputing paradigms, optimization, decision making, game
theory, and foundations of mathematics and computer science.
“Mathematicians have never been comfortable handling
infinities… But an entirely new type of mathematics looks set to
by-pass the problem… Today, Yaroslav Sergeyev, a mathematician at
the University of Calabria in Italy solves this problem… ” MIT
Technology Review “These ideas and future hardware prototypes may
be productive in all fields of science where infinite and
infinitesimal numbers (derivatives, integrals, series, fractals)
are used.” A. Adamatzky, Editor-in-Chief of
the International Journal of Unconventional Computing. “I
am sure that the new approach … will have a very deep impact both
on Mathematics and Computer Science.” D.
Trigiante, Computational Management Science. “Within the
grossone framework, it becomes feasible to deal computationally
with infinite quantities, in a way that is both new (in the sense
that previously intractable problems become amenable to
computation) and natural”. R. Gangle, G. Caterina, F.
Tohmé, Soft Computing. “The computational features offered
by the Infinity Computer allow us to dynamically change the
accuracy of representation and floating-point operations during the
flow of a computation. When suitably implemented, this possibility
turns out to be particularly advantageous when solving
ill-conditioned problems. In fact, compared with a standard
multi-precision arithmetic, here the accuracy is improved only when
needed, thus not affecting that much the overall computational
effort.” P. Amodio, L. Brugnano, F. Iavernaro & F.
Mazzia, Soft Computing
This volume explores the connections between mathematical modeling,
computational methods, and high performance computing, and how
recent developments in these areas can help to solve complex
problems in the natural sciences and engineering. The content of
the book is based on talks and papers presented at the conference
Modern Mathematical Methods and High Performance Computing in
Science & Technology (M3HPCST), held at Inderprastha
Engineering College in Ghaziabad, India in January 2020. A wide
range of both theoretical and applied topics are covered in detail,
including the conceptualization of infinity, efficient domain
decomposition, high capacity wireless communication, infectious
disease modeling, and more. These chapters are organized around the
following areas: Partial and ordinary differential equations
Optimization and optimal control High performance and scientific
computing Stochastic models and statistics Recent Trends in
Mathematical Modeling and High Performance Computing will be of
interest to researchers in both mathematics and engineering, as
well as to practitioners who face complex models and extensive
computations.
This volume explores the connections between mathematical modeling,
computational methods, and high performance computing, and how
recent developments in these areas can help to solve complex
problems in the natural sciences and engineering. The content of
the book is based on talks and papers presented at the conference
Modern Mathematical Methods and High Performance Computing in
Science & Technology (M3HPCST), held at Inderprastha
Engineering College in Ghaziabad, India in January 2020. A wide
range of both theoretical and applied topics are covered in detail,
including the conceptualization of infinity, efficient domain
decomposition, high capacity wireless communication, infectious
disease modeling, and more. These chapters are organized around the
following areas: Partial and ordinary differential equations
Optimization and optimal control High performance and scientific
computing Stochastic models and statistics Recent Trends in
Mathematical Modeling and High Performance Computing will be of
interest to researchers in both mathematics and engineering, as
well as to practitioners who face complex models and extensive
computations.
Everything should be made as simple as possible, but not simpler.
(Albert Einstein, Readers Digest, 1977) The modern practice of
creating technical systems and technological processes of high
effi.ciency besides the employment of new principles, new
materials, new physical effects and other new solutions ( which is
very traditional and plays the key role in the selection of the
general structure of the object to be designed) also includes the
choice of the best combination for the set of parameters
(geometrical sizes, electrical and strength characteristics, etc.)
concretizing this general structure, because the Variation of these
parameters ( with the structure or linkage being already set
defined) can essentially affect the objective performance indexes.
The mathematical tools for choosing these best combinations are
exactly what is this book about. With the advent of computers and
the computer-aided design the pro bations of the selected variants
are usually performed not for the real examples ( this may require
some very expensive building of sample op tions and of the special
installations to test them ), but by the analysis of the
corresponding mathematical models. The sophistication of the
mathematical models for the objects to be designed, which is the
natu ral consequence of the raising complexity of these objects,
greatly com plicates the objective performance analysis. Today, the
main (and very often the only) available instrument for such an
analysis is computer aided simulation of an object's behavior,
based on numerical experiments with its mathematical model.
Everything should be made as simple as possible, but not simpler.
(Albert Einstein, Readers Digest, 1977) The modern practice of
creating technical systems and technological processes of high
effi.ciency besides the employment of new principles, new
materials, new physical effects and other new solutions ( which is
very traditional and plays the key role in the selection of the
general structure of the object to be designed) also includes the
choice of the best combination for the set of parameters
(geometrical sizes, electrical and strength characteristics, etc.)
concretizing this general structure, because the Variation of these
parameters ( with the structure or linkage being already set
defined) can essentially affect the objective performance indexes.
The mathematical tools for choosing these best combinations are
exactly what is this book about. With the advent of computers and
the computer-aided design the pro bations of the selected variants
are usually performed not for the real examples ( this may require
some very expensive building of sample op tions and of the special
installations to test them ), but by the analysis of the
corresponding mathematical models. The sophistication of the
mathematical models for the objects to be designed, which is the
natu ral consequence of the raising complexity of these objects,
greatly com plicates the objective performance analysis. Today, the
main (and very often the only) available instrument for such an
analysis is computer aided simulation of an object's behavior,
based on numerical experiments with its mathematical model."
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Numerical Computations: Theory and Algorithms - Third International Conference, NUMTA 2019, Crotone, Italy, June 15-21, 2019, Revised Selected Papers, Part II (Paperback, 1st ed. 2020)
Yaroslav D. Sergeyev, Dmitri E. Kvasov
|
R1,639
Discovery Miles 16 390
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Ships in 10 - 15 working days
|
The two-volume set LNCS 11973 and 11974 constitute revised selected
papers from the Third International Conference on Numerical
Computations: Theory and Algorithms, NUMTA 2019, held in Crotone,
Italy, in June 2019. This volume, LNCS 11974, consists of 19 full
and 32 short papers chosen among regular papers presented at the
the Conference including also the paper of the winner (Lorenzo
Fiaschi, Pisa, Italy) of The Springer Young Researcher Prize for
the best NUMTA 2019 presentation made by a young scientist. The
papers in part II explore the advanced research developments in
such interconnected fields as local and global optimization,
machine learning, approximation, and differential equations. A
special focus is given to advanced ideas related to methods and
applications using emerging computational paradigms.
|
Numerical Computations: Theory and Algorithms - Third International Conference, NUMTA 2019, Crotone, Italy, June 15-21, 2019, Revised Selected Papers, Part I (Paperback, 1st ed. 2020)
Yaroslav D. Sergeyev, Dmitri E. Kvasov
|
R1,668
Discovery Miles 16 680
|
Ships in 10 - 15 working days
|
The two-volume set LNCS 11973 and 11974 constitute revised selected
papers from the Third International Conference on Numerical
Computations: Theory and Algorithms, NUMTA 2019, held in Crotone,
Italy, in June 2019. This volume, LNCS 11973, consists of 34 full
and 18 short papers chosen among papers presented at special
streams and sessions of the Conference. The papers in part I were
organized following the topics of these special sessions:
approximation: methods, algorithms, and applications; computational
methods for data analysis; first order methods in optimization:
theory and applications; high performance computing in modelling
and simulation; numbers, algorithms, and applications; optimization
and management of water supply.
This book provides a friendly introduction to the paradigm and
proposes a broad panorama of killing applications of the Infinity
Computer in optimization: radically new numerical algorithms, great
theoretical insights, efficient software implementations, and
interesting practical case studies. This is the first book
presenting to the readers interested in optimization the advantages
of a recently introduced supercomputing paradigm that allows to
numerically work with different infinities and infinitesimals on
the Infinity Computer patented in several countries. One of the
editors of the book is the creator of the Infinity Computer, and
another editor was the first who has started to use it in
optimization. Their results were awarded by numerous scientific
prizes. This engaging book opens new horizons for researchers,
engineers, professors, and students with interests in
supercomputing paradigms, optimization, decision making, game
theory, and foundations of mathematics and computer science.
"Mathematicians have never been comfortable handling infinities...
But an entirely new type of mathematics looks set to by-pass the
problem... Today, Yaroslav Sergeyev, a mathematician at the
University of Calabria in Italy solves this problem... " MIT
Technology Review "These ideas and future hardware prototypes may
be productive in all fields of science where infinite and
infinitesimal numbers (derivatives, integrals, series, fractals)
are used." A. Adamatzky, Editor-in-Chief of the International
Journal of Unconventional Computing. "I am sure that the new
approach ... will have a very deep impact both on Mathematics and
Computer Science." D. Trigiante, Computational Management Science.
"Within the grossone framework, it becomes feasible to deal
computationally with infinite quantities, in a way that is both new
(in the sense that previously intractable problems become amenable
to computation) and natural". R. Gangle, G. Caterina, F. Tohme,
Soft Computing. "The computational features offered by the Infinity
Computer allow us to dynamically change the accuracy of
representation and floating-point operations during the flow of a
computation. When suitably implemented, this possibility turns out
to be particularly advantageous when solving ill-conditioned
problems. In fact, compared with a standard multi-precision
arithmetic, here the accuracy is improved only when needed, thus
not affecting that much the overall computational effort." P.
Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing
|
Learning and Intelligent Optimization - 11th International Conference, LION 11, Nizhny Novgorod, Russia, June 19-21, 2017, Revised Selected Papers (Paperback, 1st ed. 2017)
Roberto Battiti, Dmitri E. Kvasov, Yaroslav D. Sergeyev
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R2,752
Discovery Miles 27 520
|
Ships in 10 - 15 working days
|
This book constitutes the thoroughly refereed post-conference
proceedings of the 11th International Conference on Learning and
Intelligent Optimization, LION 11, held in Nizhny,Novgorod, Russia,
in June 2017. The 20 full papers (among these one GENOPT paper) and
15 short papers presented have been carefully reviewed and selected
from 73 submissions. The papers explore the advanced research
developments in such interconnected fields as mathematical
programming, global optimization, machine learning, and artificial
intelligence. Special focus is given to advanced ideas,
technologies, methods, and applications in optimization and machine
learning.
Introduction to Global Optimization Exploiting Space-Filling Curves
provides an overview of classical and new results pertaining to the
usage of space-filling curves in global optimization. The authors
look at a family of derivative-free numerical algorithms applying
space-filling curves to reduce the dimensionality of the global
optimization problem; along with a number of unconventional ideas,
such as adaptive strategies for estimating Lipschitz constant,
balancing global and local information to accelerate the search.
Convergence conditions of the described algorithms are studied in
depth and theoretical considerations are illustrated through
numerical examples. This work also contains a code for implementing
space-filling curves that can be used for constructing new global
optimization algorithms. Basic ideas from this text can be applied
to a number of problems including problems with multiextremal and
partially defined constraints and non-redundant parallel
computations can be organized. Professors, students, researchers,
engineers, and other professionals in the fields of pure
mathematics, nonlinear sciences studying fractals, operations
research, management science, industrial and applied mathematics,
computer science, engineering, economics, and the environmental
sciences will find this title useful .
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