Titlebook: Topics in Numerical Analysis; With Special Emphasi Goetz Alefeld,Xiaojun Chen Conference proceedings 2001 Springer-Verlag Wien 2001 algorit

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A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Element,de the basic idea and outline the concept of verification procedures as well as show the final numerical result. The detailed description of procedures for actual computations will be presented in the forthcoming paper [11].

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A Survey of Robust Preconditioning Methods, in the construction of such preconditioners. The paper gives a background to the methods and gives some more detailed examples of some of the methods when used for symmetric and positive definite matrices.

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A Box-Constrained Optimization Algorithm with Negative Curvature Directions and Spectral Projected Gradients,A practical algorithm for box-constrained optimization is introduced. The algorithm combines an active-set strategy with spectral projected gradient iterations. In the interior of each face a strategy that deals efficiently with negative curvature is employed. Global convergence results are given. Numerical results are presented.

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A Superlinearly and Globally Convergent Method for Reaction and Diffusion Problems with a Non-Lipschitzian Operator,This paper proposes a superlinearly and globally convergent method for reaction and diffusion problems with a non-Lipschitz operator. We reformulate the problem as a system of equations with locally Lipschitzian functions. Then the system is solved by using a smoothing Newton method which converges superlinearly and globally.

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