# Iterative Methods for Large Linear Systems.

##### By: Kincaid, David R.

##### Contributor(s): Hayes, Linda J.

Material type: TextSeries: eBooks on Demand.Publisher: Burlington : Elsevier Science, 2014Description: 1 online resource (350 p.).ISBN: 9781483260204.Subject(s): Iterative methods (Mathematics) | Iterative methods (Mathematics) -- Congresses | Parallel processing (Electronic computers) -- Congresses | Vector processing (Computer science) | Vector processing (Computer science) -- CongressesGenre/Form: Electronic books.Additional physical formats: Print version:: Iterative Methods for Large Linear SystemsDDC classification: 519.5/42 | 519.542 Online resources: Click here to view this ebook.Item type | Current location | Call number | URL | Status | Date due | Barcode |
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Electronic Book | UT Tyler Online Online | QA279.4 .S743 2014 (Browse shelf) | http://uttyler.eblib.com/patron/FullRecord.aspx?p=1901617 | Available | EBL1901617 |

Front Cover; Iterative Methods for Large Linear Systems; Copyright Page; Preface; Authors of Chapters; Papers Presented at Conference; Professor David M. Young, Jr.; Photographs from Conference; Table of Contents; Chapter1. Fourier Analysis of Two-Level Hierarchical Basis Preconditioners; 1 Introduction; 21D, Linear S; 3 2D, Bilinear S, Bilinear A; 4 2D, Bilinear, 5-Point A; 5 3D, Trilinear S, 7-Point A; 6 Concluding Remarks; Acknowledgements; References; Chapter 2. An Algebraic Framework for Hierarchical Basis Functions Multilevel Methods or the Search for 'Optimal'Preconditioners

1 Introduction2 The Algebraic Framework for Two-Level Hierarchical Basis FunctionMethods; 3 Recursive Definition of Preconditioner; 4 The Relative Condition Number of Mwith Respect to A; 5 Concluding Remarks; References; Chapter 3.ELLPACK and ITPACK as Research Tools for Solving Elliptic Problems; 1 Background; 2 ELLPACK andITPACK; 3 Some Basic Questions; 4 Direct vs. Iterative Methods; 5 Different Elliptic Problems; 6Symmetry; 7 Extended Network Analogy; 8 Orders of Accuracy; 9 Choice of Mesh; 10 Computational Complexity; 11 3D Problems; Acknowledgement; References

Chapter 4. Preconditioned Iterative Methods for Indefinite Symmetric ToeplitzSystems1 Introduction; 2 Toeplitz and Circulant Matrices; 3 Solution Methods; 4 Test Matrix Preconditioners; 5 Test Matrices; 6 Computed Spectra; Acknowlegements; References; Chapter 5.A Local Relaxation Scheme (Ad-Hoc SOR) Applied to Nine Pointand Block Difference Equations; 1 History; 2 The Method; 3 Nine Point Application: Cross Derivatives; 4 Block Iteration; Acknowledgements; References; Chapter 6. Block Iterative Methods for Cyclically Reduced Non-Self-AdjointElliptic Problems; 1 Introduction

2 The Reduced System for the Convection-Diffusion Equation3 Bounds for Solving the Convection-Diffusion Equation; 4 Numerical Expe; Acknowledgements; References; Chapter 7.Toward an Effective Two-Parameter SOR Method; 1 Background; 2 Singular Value Decomposition and Orthogonal Similarities; 3 Two-Parameter SOR; 4 A Numerical Example; Acknowledgements; References; Appendix; Chapter 8. Relaxation Parameters for the IQE Iterative Procedure for Solving Semi-Implicit Navier-StokesDifference Equations; 1 Introduction; 2 The Continuous and Discrete Problems; 3 The IQE Iterative Method

4 The Calculation ofw5 Numerical Results; Acknowledgements; References; Chapter 9.Hodie Approximation of Boundary Conditions; 1 Introduction; 2 Approximation 'Away from the Boundary' ; 3 Hodie as Interpolation; 4 Boundary Conditions; 5 Extension of Ui,j toΩ; 6 Indexing of Unknowns; 7 Eigenproblems; Acknowledgements; References; Chapter 10.Iterative Methods for Nonsymmetric Linear Systems; 1 Introduction; 2 Projection Methods; 3 Krylov Projection Methods; 4 Semi-Krylov Projection Methods; 5 Non-polynomial Projection Methods; 6 Non-projection Polynomial Methods; 7 Conclusion; Acknowledgements

References

Iterative Methods for Large Linear Systems

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