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Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications Vital Source e-bog
Daniele Bertaccini
(2018)
Taylor & Francis
699,00 kr.
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Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications
Daniele Bertaccini og Fabio Durastante
(2018)
Sprog: Engelsk
CRC Press LLC
1.948,00 kr.
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Detaljer om varen
- 1. Udgave
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Taylor & Francis (Februar 2018)
- ISBN: 9781351649612
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
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Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
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Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Hardback: 374 sider
- Udgiver: CRC Press LLC (Februar 2018)
- Forfattere: Daniele Bertaccini og Fabio Durastante
- ISBN: 9781498764162
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems.
The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
1 Introduction and Motivations
1.1 Notes on error analysis
1.2 Sparse matrices
1.3 On parallel computing and hardware acceleration 2 Some iterative algorithms for linear systems
2.1 Iterative algorithms and simple one-dimensional techniques
2.2 Krylov subspace algorithms, orthogonal projections: CG and GMRES
2.3 Krylov subspace algorithms, oblique projections: BiCG, QMR, CGS, BiCGstab, BiCGstab
2.4 Which Krylov method should I use? 3 General purpose preconditioning strategies
3.1 Generalities on preconditioning
3.2 Krylov iterative methods for preconditioned iterations
3.3 On Jacobi, SOR, and SSOR preconditioners
3.4 Incomplete factorizations preconditioners
3.5 Approximate Inverse Preconditioners
3.6 Preconditioning sequences of linear systems
3.7 Parallelizing preconditioners and available software
3.8 Which general purpose preconditioner should I use? 4 Preconditioners for some structured linear systems
4.1 Toeplitz and block Toeplitz systems
4.2 Notes on multigrid preconditioning
4.3 Complex symmetric systems
4.4 Saddle point systems Appendix A: A Review of Numerical Linear Algebra A.1 Vector and matrix norms A.2 Eigenvalues and singular values Appendix B: Data sets and software codes B.1 Test matrices and data sets B.2 Numerical Linear Algebra software
1.1 Notes on error analysis
1.2 Sparse matrices
1.3 On parallel computing and hardware acceleration 2 Some iterative algorithms for linear systems
2.1 Iterative algorithms and simple one-dimensional techniques
2.2 Krylov subspace algorithms, orthogonal projections: CG and GMRES
2.3 Krylov subspace algorithms, oblique projections: BiCG, QMR, CGS, BiCGstab, BiCGstab
2.4 Which Krylov method should I use? 3 General purpose preconditioning strategies
3.1 Generalities on preconditioning
3.2 Krylov iterative methods for preconditioned iterations
3.3 On Jacobi, SOR, and SSOR preconditioners
3.4 Incomplete factorizations preconditioners
3.5 Approximate Inverse Preconditioners
3.6 Preconditioning sequences of linear systems
3.7 Parallelizing preconditioners and available software
3.8 Which general purpose preconditioner should I use? 4 Preconditioners for some structured linear systems
4.1 Toeplitz and block Toeplitz systems
4.2 Notes on multigrid preconditioning
4.3 Complex symmetric systems
4.4 Saddle point systems Appendix A: A Review of Numerical Linear Algebra A.1 Vector and matrix norms A.2 Eigenvalues and singular values Appendix B: Data sets and software codes B.1 Test matrices and data sets B.2 Numerical Linear Algebra software
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