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Produktbild: Iterative Methods for Solving Linear Systems

Iterative Methods for Solving Linear Systems

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Beschreibung

Focusing on the analysis of iterative methods, the author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal,...

Beschreibung

Focusing on the analysis of iterative methods, the author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal?

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

01.01.1987
Seitenzahl

234
Maße (L/B/H)

25,3/17,8/1,3 cm

Produktdetails

Einband

Taschenbuch
Erscheinungsdatum

01.01.1987
Seitenzahl

234
Maße (L/B/H)

25,3/17,8/1,3 cm
Gewicht

422 g
Sprache

Englisch
ISBN

978-0-89871-396-1
Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Iterative Methods for Solving Linear Systems


    • List of Algorithms

    • Preface

    • Chapter 1: Introduction. Brief Overview of the State of the Art

    • Notation

    • Review of Relevant Linear Algebra

    • Part I: Krylov Subspace Approximations. Chapter 2: Some Iteration Methods. Simple Iteration

    • Orthomin(1) and Steepest Descent

    • Orthomin(2) and CG

    • Orthodir, MINRES, and GMRES

    • Derivation of MINRES and CG from the Lanczos Algorithm

    • Chapter 3: Error Bounds for CG, MINRES, and GMRES. Hermitian Problems—CG and MINRES

    • Non-Hermitian Problems—GMRES

    • Chapter 4: Effects of Finite Precision Arithmetic. Some Numerical Examples

    • The Lanczos Algorithm

    • A Hypothetical MINRES/CG Implementation

    • A Matrix Completion Problem

    • Orthogonal Polynomials

    • Chapter 5: BiCG and Related Methods. The Two-Sided Lanczos Algorithm

    • The Biconjugate Gradient Algorithm

    • The Quasi-Minimal Residual Algorithm

    • Relation Between BiCG and QMR

    • The Conjugate Gradient Squared Algorithm

    • The BiCGSTAB Algorithm

    • Which Method Should I Use?

    • Chapter 6: Is There A Short Recurrence for a Near-Optimal Approximation? The Faber and Manteuffel Result

    • Implications

    • Chapter 7: Miscellaneous Issues. Symmetrizing the Problem

    • Error Estimation and Stopping Criteria

    • Attainable Accuracy

    • Multiple Right-Hand Sides and Block Methods

    • Computer Implementation

    • Part II: Preconditioners. Chapter 8: Overview and Preconditioned Algorithms. Chapter 9: Two Example Problems. The Diffusion Equation

    • The Transport Equation

    • Chapter 10: Comparison of Preconditioners. Jacobi, Gauss--Seidel, SOR

    • The Perron--Frobenius Theorem

    • Comparison of Regular Splittings

    • Regular Splittings Used with the CG Algorithm

    • Optimal Diagonal and Block Diagonal Preconditioners

    • Chapter 11: Incomplete Decompositions. Incomplete Cholesky Decomposition

    • Modified Incomplete Cholesky Decomposition

    • Chapter 12: Multigrid and Domain Decomposition Methods. Multigrid Methods

    • Basic Ideas of Domain Decomposition Methods.