國立高雄大學圖資館 |

登入

回首頁

Krylov subspace methods for linear systemsprinciples of algorithms /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Krylov subspace methods for linear systemsby Tomohiro Sogabe.
其他題名:	principles of algorithms /
作者:	Sogabe, Tomohiro.
出版者:	Singapore :Springer Nature Singapore :2022.
面頁冊數:	xiii, 225 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Linear systems.
電子資源:	https://doi.org/10.1007/978-981-19-8532-4
ISBN:	9789811985324$q(electronic bk.)

Krylov subspace methods for linear systemsprinciples of algorithms /
Sogabe, Tomohiro.

Krylov subspace methods for linear systemsprinciples of algorithms /[electronic resource] :by Tomohiro Sogabe. - Singapore :Springer Nature Singapore :2022. - xiii, 225 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v. 602198-3712 ;. - Springer series in computational mathematics ;42..

Introduction to Numerical Methods for Solving Linear Systems -- Some Applications to Computational Science and Data Science -- Classiﬁcation and Theory of Krylov Subspace Methods -- Applications to Shifted Linear Systems -- Applications to Matrix Functions.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000) Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.

ISBN: 9789811985324$q(electronic bk.)

Standard No.: 10.1007/978-981-19-8532-4doiSubjects--Topical Terms:

182249
Linear systems.

LC Class. No.: QA402 / .S64 2022

Dewey Class. No.: 003.74

Krylov subspace methods for linear systemsprinciples of algorithms /
LDR:02722nmm a2200337 a 4500 001 634546
003 DE-He213
005 20230120100921.0
006 m d
007 cr nn 008maaau
008 230529s2022 si s 0 eng d
020 $a 9789811985324$q(electronic bk.)
020 $a 9789811985317$q(paper)
024 7 $a 10.1007/978-981-19-8532-4 $2 doi
035 $a 978-981-19-8532-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402 $b .S64 2022
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 003.74 $2 23
090 $a QA402 $b .S682 2022
100 1 $a Sogabe, Tomohiro. $3 940998
245 1 0 $a Krylov subspace methods for linear systems $h [electronic resource] : $b principles of algorithms / $c by Tomohiro Sogabe.
260 $a Singapore : $c 2022. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xiii, 225 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in computational mathematics, $x 2198-3712 ; $v v. 60
505 0 $a Introduction to Numerical Methods for Solving Linear Systems -- Some Applications to Computational Science and Data Science -- Classiﬁcation and Theory of Krylov Subspace Methods -- Applications to Shifted Linear Systems -- Applications to Matrix Functions.
520 $a This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000) Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.
650 0 $a Linear systems. $3 182249
650 0 $a Numerical analysis. $3 182073
650 0 $a Algorithms. $3 184661
650 1 4 $a Numerical Analysis. $3 275681
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer series in computational mathematics ; $v 42. $3 560664
856 4 0 $u https://doi.org/10.1007/978-981-19-8532-4
950 $a Mathematics and Statistics (SpringerNature-11649)