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91.
Ljubomir iri Arif Rafiq Nenad Caki 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4332-4337
In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383–429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363–1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume. 相似文献
92.
This paper presents a computer-based method for optimally sizing members of planar steel frameworks using commercially available standard sections. For first-order behavior and static loads, a minimum-weight structure is found while simultaneously ensuring stress and displacement performance conditions under applied service loads. Architectural conditions are imposed on section sizes to satisfy fabrication requirements related to member continuity and structure symmetry. The design method presented is iterative in nature and remarkably efficient. The number of iterations is generally quite small and almost totally independent: of the complexity of the structure. Designs are presented for two steel frameworks that are typical of those encountered in professional practise. 相似文献
93.
Constantin Popa 《BIT Numerical Mathematics》1999,39(2):323-338
In this paper we present an algorithm which, for a given (sparse) matrix, constructs a partition of its set of row-indices, such that each subset of this partition (except the last one obtained) contains indices which correspond to mutually orthogonal rows. We then use such decompositions in some classes of block-projections methods, previously extended by the author to general inconsistent linear least-squares problems. Numerical experiments on an inconsistent and rank-deficient least-squares model problem are described in the last section of the paper. 相似文献
94.
张石生 《应用数学和力学(英文版)》2001,22(1):25-34
IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E → 2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉 =‖x‖·‖f‖ , ‖f‖ =‖x‖ (x∈E) . Ddfinition 1 1 LetT :D →Dbeamapping1 )Tissaidtobeasymptoticallyno… 相似文献
95.
Ulrich Kohlenbach 《Journal of Mathematical Analysis and Applications》2003,279(2):531-544
In Numer. Funct. Anal. Optim. 22 (2001) 641-656, we obtained an effective quantitative analysis of a theorem due to Borwein, Reich, and Shafrir on the asymptotic behavior of general Krasnoselski-Mann iterations for nonexpansive self-mappings of convex sets C in arbitrary normed spaces. We used this result to obtain a new strong uniform version of Ishikawa's theorem for bounded C. In this paper we give a qualitative improvement of our result in the unbounded case and prove the uniformity result for the bounded case under the weaker assumption that C contains a point x whose Krasnoselski-Mann iteration (xk) is bounded. We also consider more general iterations for which asymptotic regularity is known only for uniformly convex spaces (Groetsch). We give uniform effective bounds for (an extension of) Groetsch's theorem which generalize previous results by Kirk, Martinez-Yanez, and the author. 相似文献
96.
In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained show that the bigger the parameter k is(i.e., we select the more upper right diagonal elements to be the preconditioner), the less the spectral radius of iterative matrix is. A numerical example generated randomly is provided to illustrate the theoretical results. 相似文献
97.
强伪压缩算子带误差的Ishikawa迭代的强稳定性 总被引:2,自引:0,他引:2
设X是任意实Banach空间,T:X→X是一Lipschitz强伪压缩算子,本给出T带误差的Ishikawa迭代过程的强稳定性,并给出一个涉及Lipschitz强增生算子T的非线性方程Tx=f迭代解的强稳定性。 相似文献
98.
99.
Volker John 《国际流体数值方法杂志》2006,50(7):845-862
This paper studies the efficiency of two ways to treat the non‐linear convective term in the time‐dependent incompressible Navier–Stokes equations and of two multigrid approaches for solving the arising linear algebraic saddle point problems. The Navier–Stokes equations are discretized by a second‐order implicit time stepping scheme and by inf–sup stable, higher order finite elements in space. The numerical studies are performed at a 3D flow around a cylinder. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
100.
Perturbation theory in a framework of iteration methods 总被引:1,自引:0,他引:1
In a previous paper [J. Phys. A 36 (2003) 11807], we introduced the ‘asymptotic iteration method’ for solving second-order homogeneous linear differential equations. In this Letter, we study perturbed problems in quantum mechanics and we use the method to find the coefficients in the perturbation series for the eigenvalues and eigenfunctions directly, without first solving the unperturbed problem. 相似文献