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· 제목 : Iterative Methods for Solving Linear Systems (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 응용수학
· ISBN : 9780898713961
· 쪽수 : 234쪽
· 출판일 : 1987-01-01
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 응용수학
· ISBN : 9780898713961
· 쪽수 : 234쪽
· 출판일 : 1987-01-01
목차
- 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.
