Matrix preconditioning techniques and applications /
Chen, Ke, 1962-
Matrix preconditioning techniques and applications / Matrix Preconditioning Techniques & Applications Ke Chen. - Cambridge : Cambridge University Press, 2005. - 1 online resource (xxiii, 568 pages) : digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ; 19 . - Cambridge monographs on applied and computational mathematics ; 19. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Introduction -- Direct methods -- Iterative methods -- Matrix splitting preconditioners [T1] : direct approximation of A[subscript nxn] -- Approximate inverse preconditioners [T2] : direct approximation of A[subscript nxn][superscript -1] -- Multilevel methods and preconditioners [T3] : coarse grid approximation -- Multilevel recursive Schur complements preconditioners [T4] -- Sparse wavelet preconditioners [T5] : approximation of A[subscript nxn] and A[subscript nxn][superscript -1] -- Wavelet Schur preconditioners [T6] -- Implicit wavelet preconditioners [T7} -- Application I : acoustic scattering modelling -- Application II : coupled matrix problems. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
9780511543258 (ebook)
Differential equations--Numerical solutions--Data processing.
Iterative methods (Mathematics)--Data processing.
Integral equations--Numerical solutions--Data processing.
Sparse matrices--Data processing.
QA188 / .C455 2005
512.9434
Matrix preconditioning techniques and applications / Matrix Preconditioning Techniques & Applications Ke Chen. - Cambridge : Cambridge University Press, 2005. - 1 online resource (xxiii, 568 pages) : digital, PDF file(s). - Cambridge monographs on applied and computational mathematics ; 19 . - Cambridge monographs on applied and computational mathematics ; 19. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Introduction -- Direct methods -- Iterative methods -- Matrix splitting preconditioners [T1] : direct approximation of A[subscript nxn] -- Approximate inverse preconditioners [T2] : direct approximation of A[subscript nxn][superscript -1] -- Multilevel methods and preconditioners [T3] : coarse grid approximation -- Multilevel recursive Schur complements preconditioners [T4] -- Sparse wavelet preconditioners [T5] : approximation of A[subscript nxn] and A[subscript nxn][superscript -1] -- Wavelet Schur preconditioners [T6] -- Implicit wavelet preconditioners [T7} -- Application I : acoustic scattering modelling -- Application II : coupled matrix problems. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
9780511543258 (ebook)
Differential equations--Numerical solutions--Data processing.
Iterative methods (Mathematics)--Data processing.
Integral equations--Numerical solutions--Data processing.
Sparse matrices--Data processing.
QA188 / .C455 2005
512.9434