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Iterative solution of large sparse systems of equations[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	518.26
書名/作者:	Iterative solution of large sparse systems of equations/ by Wolfgang Hackbusch.
作者:	Hackbusch, Wolfgang.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xxiii, 509 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Iterative methods (Mathematics)
標題:	Differential equations, Partial - Numerical solutions.
標題:	Mathematics.
標題:	Numerical Analysis.
標題:	Linear and Multilinear Algebras, Matrix Theory.
標題:	Partial Differential Equations.
ISBN:	9783319284835
ISBN:	9783319284811
內容註:	Part I: Linear Iterations -- Introduction -- Iterative Methods -- Classical Linear Iterations in the Positive Definite Case -- Analysis of Classical Iterations Under Special Structural Conditions -- Algebra of Linear Iterations -- Analysis of Positive Definite Iterations -- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods -- Semi-Iterative Methods -- Gradient Methods -- Conjugate Gradient Methods and Generalizations -- Part III: Special Iterations -- Multigrid Iterations -- Domain Decomposition and Subspace Methods -- H-LU Iteration -- Tensor-based Methods -- Appendices.
摘要、提要註:	In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
電子資源:	http://dx.doi.org/10.1007/978-3-319-28483-5

Iterative solution of large sparse systems of equations[electronic resource] /
Hackbusch, Wolfgang.

Iterative solution of large sparse systems of equations[electronic resource] /by Wolfgang Hackbusch. - 2nd ed. - Cham :Springer International Publishing :2016. - xxiii, 509 p. :ill., digital ;24 cm. - Applied mathematical sciences,v.950066-5452 ;. - Applied mathematical sciences ;v.176..

Part I: Linear Iterations -- Introduction -- Iterative Methods -- Classical Linear Iterations in the Positive Definite Case -- Analysis of Classical Iterations Under Special Structural Conditions -- Algebra of Linear Iterations -- Analysis of Positive Definite Iterations -- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods -- Semi-Iterative Methods -- Gradient Methods -- Conjugate Gradient Methods and Generalizations -- Part III: Special Iterations -- Multigrid Iterations -- Domain Decomposition and Subspace Methods -- H-LU Iteration -- Tensor-based Methods -- Appendices.

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

ISBN: 9783319284835

Standard No.: 10.1007/978-3-319-28483-5doiSubjects--Topical Terms:

404166
Iterative methods (Mathematics)

LC Class. No.: QA297.8

Dewey Class. No.: 518.26

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