2 edition of Iterative methods for a class of large, sparse, nonsymmetric linear systems found in the catalog.
Iterative methods for a class of large, sparse, nonsymmetric linear systems
Written in English
Thesis(Ph.D.) - Loughborough University of Technology.
|Statement||by Changjun Li.|
The ﬁeld of iterative methods for solving systems of linear equations is in constant ﬂux, with new methods and approaches continually being created, modiﬁed, tuned, and some eventually discarded. We expect the material in this book to undergo changes from time to time as some of these new approaches mature and become the state-of-the-art. Iterative Methods for Sparse Linear Systems (The Pws Series in Computer Science) by Saad, Yousef. out of 5 stars The first book you should read on iterative methods. Reviewed in the United States on Septem Iterative Solution of Large Sparse Systems of Equations (Applied Mathematical Sciences) by Wolfgang Hackbusch.
Also I have used this book for my class as main textbook along with "Iterative Methods for Solving Linear and Nonlinear Equations" by C. T. Kelley, which is another SIAM book. Highly recommended. 3 people found this helpful. This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.
From your link, it seems that Microsoft's Solver Foundation is a linear and nonlinear optimization library, which is connected to numerical linear algebra, but is not the right tool for solving the linear system Ax = b for the vector x given a sparse matrix A and the vector b. – las3rjock Feb 28 '10 at Iterative methods for linear systems In ﬁnite-element method, we express our solution as a linear combination u k of basis functions Typically, these iterative methods are based on a splitting of A. This is a decomposition A = M −K, where M is non-singular. Any splitting creates a possible iterative .
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Iterative methods for large, sparse, nonsymmetric systems of linear equations. Iterative methods for large, sparse, nonsymmetric systems of linear equations.
Computing methodologies. Symbolic and algebraic manipulation. Symbolic and algebraic algorithms. Linear algebra algorithms.
Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers.
Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods.
Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. Matrices. For the sake of generality, all vector spaces considered in this chapter are complex, unless otherwise stated.
A complex n×mmatrix Ais an n×marray of complex numbers aij, i= 1,n,j= 1,m. The set of all n×mmatrices is a complex vector space denoted by Cn×m. Mayer J () A numerical evaluation of preprocessing and ILU-type preconditioners for the solution of unsymmetric sparse linear systems using iterative methods, ACM Transactions on Mathematical Software,(), Online publication date: 1-Mar An important example of such a method is the biconjugate gradient method described in the next section.
Iterative Methods for Nonsymmetric Linear Systems Examples of Krylov Projection Method Within the class of Krylov projection methods nonsymmetric linear systems book three important subclasses, de fined by restrictions applied to by: This chapter discusses the selection of an iterative method that can be used in solving the large linear system Au = b (1), where A is a large sparse positive definite matrix.
It also highlights the case where the system (corresponds to the finite difference solution of a self-adjoint elliptic partial differential equation. SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () An iterative solution method for solving sparse nonsymmetric linear by: We consider a class of iterative algorithms for solving systems of linear equations where the coefficient matrix is nonsymmetric with positive-definite symmetric part.
The algorithms are modelled after the conjugate gradient method, and are well suited for large sparse systems. They do not make use of any associated symmetric problems. Iterative methods for solving general, large sparse linear systems have been gaining popularity in many areas of scientiﬁc computing.
Until recently, direct solution methods were often preferred to iterative methods in real applications because of their robustness and predictable behavior. This book on iterative methods for linear equations can b e used as a tutorial and a reference for those who need to solve sparse and/or structured large linear systems of algebraic equations.
In recent years much research has focused on the efficient solution of large sparse or structured linear systems using iterative methods. A language full of acronyms for a thousand different algorithms has developed, and it is often difficult for the nonspecialist (or sometimes even the specialist) to identify the basic principles involved.
Lanczos‐type product methods (LTPMs), in which the residuals are defined by the product of stabilizing polynomials and the Bi‐CG residuals, are effective iterative solvers for large sparse Author: Yousef Saad. Book Condition: Iterative Methods for Sparse Linear Systems by Yousef Saad.
Society for Industrial and Applied Mathematics. 2nd edition () ISBN Paperback. Some bending to covers, but no creases. Some sun-fading to covers, the spine and part of the front cover/5(9).
This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse ma-trices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.
The method works exceptionally well for the solution of large sparse systems of linear equations, the co-efficient matrix A of which need not be symmetric but should have workable splits. The method can be applied to problems which arise in convection-diffusion, flow of fluids and oil reservoir by: 4.
The first iterative methods used for solving large linear systems were based on relaxation of the coordinates. Beginning with a given approximate solution, these methods modify the components of.
Abstract. Many applications require the solution of very large systems of linear equations Ax = b in which the matrix A is fortunately sparse, i.e., has only relatively few nonzero systems arise, for instance, if difference methods or finite element methods arc being used for solving boundary value problems in partial differential equations.
Iterative methods are considered for the numerical solution of large, sparse, nonsingular, and nonsymmetric systems of linear equations Ax=b, where it is also required that A is p-cyclic (p≥2).
Firstly, it is shown that the SOR method applied to the system with A as p-cyclic, if p>2, has a slower rate of convergence than the SOR method applied to the same system with A considered as 2-cyclic Cited by: 6.
The Generalized Minimal Residual (GMRES) method [33, 34] is the most widely used algorithm for the solution of large, sparse, nonsymmetric systems of linear equations Ax = b. Starting from an. Row Projection Methods For Large Nonsymmetric Linear Systems.
textbook in the area of iterative algorithms. It is the first book to combine subjects such as optimization, convex analysis, and.Preface 1.
Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations Preconditioning techniques Parallel implementations () An EM-based iterative method for solving large sparse linear systems.
Linear and Multilinear Algebra() Deterministic Truncation of the Monte Carlo Transport Solution for Reactor Eigenvalue and Pinwise Power Distribution.