Titlebook: Iterative Solution of Large Sparse Systems of Equations; Wolfgang Hackbusch Book 2016Latest edition Springer International Publishing Swit

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Wolfgang Hackbuschhe spectacular progress of chemical research. Our food supply has not been spared from this general trend, however, and chemical sub- stances are being continuously incorporated in foodstuffs. Some of these substances are added to food for technological purposes such as pre- serving food from bacter

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Introductionhods. Deliberately, a simply structured problem is chosen since this allows us to determine all required quantities explicitly. The role of the ordering of the unknowns is explained. Section 1.3 introduces the notation for vectors and matrices. Besides the behaviour of an iterative method for a sing

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Iterative Methodshe given system of equations, as well as ., guaranteeing the success of the iteration. The most important result of this chapter is the characterisation of the convergence of linear iterations by the spectral radius of the iteration matrix (cf. §2.1.4). Since we only consider iterative methods for s

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Classical Linear Iterations in the Positive Definite Casever, is essentially different for the case of positive definite matrices . discussed below and other cases studied in Chapter 4. The introductory Section 3.1 underlines the fact that the positive definite case is of practical interest. The Poisson model matrix is an example of a positive definite ma

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Analysis of Classical Iterations Under Special Structural Conditionstructural matrix property. In Section 4.1, we consider the simpler structure of 2-cyclic matrices. Sections 4.3–4.5 investigate the Richardson, Jacobi, and Gauss–Seidel iteration in this case. Section 4.6 contains the analysis of the SOR iteration. Finally, Section 4.7 presents numerical results for

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Algebra of Linear Iterations an algebra, i.e., there are several operations defined on .. In this chapter we define the following operations: . of a linear iteration . produces the adjoint iteration .. This gives rise to the definition of symmetric and positive definite iterations in Section 5.1. . of a linear iteration . by a

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Analysis of Positive Definite Iterationsates six cases which are analysed in Section 6.2. In several cases, convergence holds for a suitably damped version of the iteration. Of particular interest are symmetric and positive definite iterations constructed in the previous chapter. In Section 6.3 we analyse traditional symmetric iterative m

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Semi-Iterative Methodssing the notion of Krylov spaces, we only require that the errors of the semi-iterates . be elements of the Krylov space .. In the second formulation of Section 8.2, the polynomials . associated with . are related either by a two-term or by a three-term recursion. Section 8.3 tries to determine the