國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Riemannian optimization and its appl...

Sato, Hiroyuki.

Riemannian optimization and its applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Riemannian optimization and its applicationsby Hiroyuki Sato.
作者:	Sato, Hiroyuki.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	ix, 129 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Riemannian manifolds.
電子資源:	https://doi.org/10.1007/978-3-030-62391-3
ISBN:	9783030623913$q(electronic bk.)

Riemannian optimization and its applications
Sato, Hiroyuki.

Riemannian optimization and its applications[electronic resource] /by Hiroyuki Sato. - Cham :Springer International Publishing :2021. - ix, 129 p. :ill., digital ;24 cm. - SpringerBriefs in electrical and computer engineering, Control, automation and robotics. - SpringerBriefs in electrical and computer engineering.Control, automation and robotics..

Chapter 1. Introduction -- Chapter 2. Preliminaries and Overview of Euclidean Optimization -- Chapter 3. Unconstrained Optimization on Riemannian Manifolds -- Chapter 4. Conjugate Gradient Methods on Riemannian Manifolds -- Chapter 5. Applications of Riemannian Optimization -- Chapter 6. Recent Developments in Riemannian Optimization.

This brief describes the basics of Riemannian optimization-optimization on Riemannian manifolds-introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields. To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.

ISBN: 9783030623913$q(electronic bk.)

Standard No.: 10.1007/978-3-030-62391-3doiSubjects--Topical Terms:

190949
Riemannian manifolds.

LC Class. No.: QA649 / .S38 2021

Dewey Class. No.: 516.373

Riemannian optimization and its applications
LDR:02470nmm a2200337 a 4500 001 600545
003 DE-He213
005 20210521115930.0
006 m d
007 cr nn 008maaau
008 211104s2021 sz s 0 eng d
020 $a 9783030623913$q(electronic bk.)
020 $a 9783030623890$q(paper)
024 7 $a 10.1007/978-3-030-62391-3 $2 doi
035 $a 978-3-030-62391-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA649 $b .S38 2021
072 7 $a TJFM $2 bicssc
072 7 $a TEC004000 $2 bisacsh
072 7 $a TJFM $2 thema
082 0 4 $a 516.373 $2 23
090 $a QA649 $b .S253 2021
100 1 $a Sato, Hiroyuki. $3 895133
245 1 0 $a Riemannian optimization and its applications $h [electronic resource] / $c by Hiroyuki Sato.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a ix, 129 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in electrical and computer engineering, Control, automation and robotics
505 0 $a Chapter 1. Introduction -- Chapter 2. Preliminaries and Overview of Euclidean Optimization -- Chapter 3. Unconstrained Optimization on Riemannian Manifolds -- Chapter 4. Conjugate Gradient Methods on Riemannian Manifolds -- Chapter 5. Applications of Riemannian Optimization -- Chapter 6. Recent Developments in Riemannian Optimization.
520 $a This brief describes the basics of Riemannian optimization-optimization on Riemannian manifolds-introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields. To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.
650 0 $a Riemannian manifolds. $3 190949
650 0 $a Mathematical optimization. $3 183292
650 1 4 $a Control and Systems Theory. $3 825946
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Statistical Theory and Methods. $3 274054
650 2 4 $a Systems Theory, Control. $3 274654
650 2 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in electrical and computer engineering. $p Control, automation and robotics. $3 592008
856 4 0 $u https://doi.org/10.1007/978-3-030-62391-3
950 $a Intelligent Technologies and Robotics (SpringerNature-42732)