國立虎尾科技大學 |

Numerical Infinities and Infinitesimals in Optimization

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Numerical Infinities and Infinitesimals in Optimization/ edited by Yaroslav D. Sergeyev, Renato De Leone.
其他作者:	Sergeyev, Yaroslav D.
面頁冊數:	XVI, 365 p. 71 illus., 38 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Engineering mathematics. -
電子資源:	https://doi.org/10.1007/978-3-030-93642-6
ISBN:	9783030936426

Numerical Infinities and Infinitesimals in Optimization
Numerical Infinities and Infinitesimals in Optimization[electronic resource] /edited by Yaroslav D. Sergeyev, Renato De Leone. - 1st ed. 2022. - XVI, 365 p. 71 illus., 38 illus. in color.online resource. - Emergence, Complexity and Computation,432194-7295 ;. - Emergence, Complexity and Computation,12.

A New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals -- Nonlinear Optimization: A Brief Overview -- The role of grossone in Nonlinear Programming and Exact Penalty Methods.

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.

ISBN: 9783030936426

Standard No.: 10.1007/978-3-030-93642-6doiSubjects--Topical Terms:

562757
Engineering mathematics.

LC Class. No.: TA329-348

Dewey Class. No.: 620

Numerical Infinities and Infinitesimals in Optimization
LDR:04252nam a22004215i 4500 001 1088249
003 DE-He213
005 20220705050501.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783030936426 $9 978-3-030-93642-6
024 7 $a 10.1007/978-3-030-93642-6 $2 doi
035 $a 978-3-030-93642-6
050 4 $a TA329-348
050 4 $a TA345-345.5
072 7 $a TBJ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a TBJ $2 thema
082 0 4 $a 620 $2 23
245 1 0 $a Numerical Infinities and Infinitesimals in Optimization $h [electronic resource] / $c edited by Yaroslav D. Sergeyev, Renato De Leone.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XVI, 365 p. 71 illus., 38 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Emergence, Complexity and Computation, $x 2194-7295 ; $v 43
505 0 $a A New Computational Paradigm Using Grossone-Based Numerical Infinities and Infinitesimals -- Nonlinear Optimization: A Brief Overview -- The role of grossone in Nonlinear Programming and Exact Penalty Methods.
520 $a 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.
650 0 $a Engineering mathematics. $3 562757
650 0 $a Engineering—Data processing. $3 1297966
650 0 $a Mathematical optimization. $3 527675
650 0 $a Calculus of variations. $3 527927
650 0 $a Mathematical statistics—Data processing. $3 1366001
650 1 4 $a Mathematical and Computational Engineering Applications. $3 1387767
650 2 4 $a Data Engineering. $3 1226308
650 2 4 $a Calculus of Variations and Optimization. $3 1366302
650 2 4 $a Statistics and Computing. $3 1366004
700 1 $a Sergeyev, Yaroslav D. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1078213
700 1 $a De Leone, Renato. $e editor. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1395396
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030936419
776 0 8 $i Printed edition: $z 9783030936433
776 0 8 $i Printed edition: $z 9783030936440
830 0 $a Emergence, Complexity and Computation, $x 2194-7287 ; $v 12 $3 1254548
856 4 0 $u https://doi.org/10.1007/978-3-030-93642-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)