The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique of generalized line search. Two conditions are given which guarantee the global convergenc...
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The convergence properties of the Fletcher-Reeves method for unconstrained optimization are further studied with the technique of generalized line search. Two conditions are given which guarantee the global convergence of the Fletcher-Reeves method using generalized Wolfe line searches or generalized Arjimo line searches, whereas an example is constructed showing that the conditions cannot be relaxed in certain senses.
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...
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By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite...
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A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.
A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of ...
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A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.
In geologically complex regions, the prestack depth migration is necessary in order to obtain accurate structure images. In this report, we discuss the prestack depth migration by finite-difference (FD) method and Fou...
The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relax...
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The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relaxation methods really have considerably larger convergence domains.
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