In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any li...
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In this paper, we discuss the convergence properties of the memoryless quasi-Newton method proposed by Shanno (1978). In the two-dimensional quadratic case, we prove the global convergence of the method without any line search; if an exact line search is made at the first iteration, then the method gives the exact solution at most at the forth iteration. Numerical experiments further demonstrate these properties of the memoryless quasi-Newton method.
In this paper, a non-overlapping domain decomposition method is discussed for solving the exterior boundary value problem of plane elasticity equation. The exterior domain is naturally decomposed by a circle into a bo...
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In this paper, a non-overlapping domain decomposition method is discussed for solving the exterior boundary value problem of plane elasticity equation. The exterior domain is naturally decomposed by a circle into a bounded domain and an unbounded domain. With the advantage of the natural boundary reduction, a D-N method is presented. This method is effective and geometric convergent. The convergence rate of this iteration is independent of the finite element mesh size, but dependent on the relaxation factor.
In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain. By studying the properties of the natural integral operator and the Poisson integral operator, we deve...
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In this paper we discuss the natural boundary element method for harmonic equation in an exterior elliptic domain. By studying the properties of the natural integral operator and the Poisson integral operator, we develop a numerical method to solve the natural integral equation. We also devise a fast algorithm for the solution of the corresponding system of linear equations. Finally we present some numerical results.
The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorit...
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The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorithm of adaptive finite element method based on this a posteriori error estimate are given.
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