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Titlebook: Computer Algorithms for Solving Linear Algebraic Equations; The State of the Art Emilio Spedicato Conference proceedings 1991 Springer-Verl

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Paul J. J. Welfens,Andreas SchwarzIn this paper we present the main properties of the class of direct methods for solving linear equations proposed by Abaffy, Broyden and Spedicato in 1984 and called the ABS class.
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Connecting the Testbench and Design,We deal with the implementation of linear algebra algorithms on distributed memory architectures such as systolic arrays and general-purpose hypercubes. Throughout, we use Gaussian elimination as a target example.
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Multi-Grid Algorithms,Multi-grid methods belong to the class of the fastest iterations, since their convergence rate is independent of the step size .. Their applicability does not require symmetry or positive definiteness. Further, it is easy to generalise multi-grid methods to nonlinear problems.
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Two Multi-Level Methods for Nonuniformly Refined Grids,The hierarchical basis method and the recent method of Bramble, Pasciak and Xu are multi-level type methods which are especially well suited for nonuniformely refined grids. The paper gives a short summary of these methods.
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Algorithms for Linear Least Squares Problems,al equations ..(.) = 0 and preconditioned are surveyed. In least squares problems arising from multidimensional models the matrices often possess a block structure, perhaps at several levels, which reflects a “local connection” structure in the underlying physical problem. For such problems parallel
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