Iterative Solution Methods Cambridge University Press, 1996 ...

Iterative Solution Methods Cambridge University Press, 1996 9780521555692 Owe Axelsson 654 pages 1996 Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning, we present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer. Iterative methods for the solution of equations, from the Preface (1964):'This book presents a general theory of iteration algorithms for the numerical solution of equations and systems of equations. The relationship between the quantity and the quality of information used by an algorithm and the efficiency. Iterative solution methods, in this chapter we give direct solution methods to solve a linear system of equations. The idea is based on elimination and given in Section 1.2. However using this method in practice shows that it has some drawbacks. First round off errors can spoil the result, second. Iterative solution methods for modeling multiphase flow in porous media fully implicitly, we discuss several fully implicit techniques for solving the nonlinear algebraic system arising in an expanded mixed finite element or cell-centered finite difference discretization of two-and three-phase porous media flow. Every outer nonlinear Newton iteration requires. A fast incremental/iterative solution procedure that handles snap-through, riks [1] has recently proposed a new solution procedure for overcoming limit points. To this end, he adds, to the standard equilibrium equations, a constraint equation fixing the length of the incremental load step in load/deflection space. The applied load level becomes. Iterative solution methods, this chapter deals with iterative methods for nonlinear ill-posed problems. We present gradient and Newton type methods as well as nonstandard iterative algorithms such as Kaczmarz, expectation maximization, and Bregman iterations. Our intention here is to cite. Iterative solution of large linear systems, flow, and weather pre- diction. The solution of a large system with a sparse matrix is usually obtained by iterative methods instead of by direct methods such as the Gauss elimination method. An extensive theory has been developed. Iterative solution methods, this presentation is intended to review the state-of-the-art of iterative methods for solving large sparse linear systems such as arising in finite difference and finite element approximations of boundary value problems. However, in order to keep this review within. Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners, or more stabilisation parameters. Although there has been some work on the optimal choice of such parameters from the point of view of solution accuracy (see [P], for example), the effect of such parameters on the rate of convergence of iterative solution methods has received. A generalization of the additive correction methods for the iterative solution of matrix equations, a general formulation of the additive correction methods of Poussin [4] and Watts [7] is presented. The methods are applied to the solution of finite difference equations resulting from elliptic and parabolic partial differential equations. A new method is developed. An iterative solution method for linear systems of which the coefficient matrix is a symmetric ð ‘ -matrix, where A is usually a sparse matrix. In this paper, iterative solution methods will be presented which are restricted to equations where A is a symmetric A/-matrix,* although symmetry is not required in most of the theorems. This. Accelerating iterative solution methods using reducedâ order models as solution predictors, we propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess. Iterative solution of nonlinear equations in several variables, the original aim of the book was to provide a reasonably comprehensive survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems, in this paper methods are described for the solution of certain sparse linear systems with a non-symmetric matrix. The power of these methods is demonstrated by extensive numerical experiments. Application of the methods is limited to problems where the matrix has only. The convergence of iterative solution methods for symmetric and indefinite linear systems, iterative solution methods provide the only feasible alternative to direct methods for very large scale linear systems such as those which derive from approximation of many partial differential equation problems. For symmetric and positive definite coefficient matrices. Mesh refinement and iterative solution methods for finite element computations, global and element residuals are introduced to determine a posteriori, computable, error bounds for finite element computations on a given mesh. The element residuals provide a criterion for determining where a finite element mesh requires refinement. This indicator. Iterative solution of implicit approximations of multidimensional partial differential equations, the Gauss-Seidel iterative method [7] is closely related to solution by successive overrelaxation [8], [15]. These two procedures are also known, respectively, as the Liebmana and extrapolated Liebmanu methods [4], [6]. Each of these two methods involves the use of a single. Templates for the solution of linear systems: building blocks for iterative methods, in this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather. Iterative solution methods, this book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear. Iterative solution methods and preconditioners for block-tridiagonal systems of equations, systems of equations arising from implicit time discretizations and finite difference space discretizations of systems of partial differential equations in two space dimensions are considered. The nonsymmetric linear systems are solved using a preconditioned CG-like.