Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal ...
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Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal and continuousmappings, and b ∈ Rn a known vector; and their global convergence are investigated in detail under weaker conditions. Some numerical computations show thatthe new methods have better convergence properties than the known ones in theliterature.
A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorith...
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A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.
In this paper, based on the mixed variational formulation in [9], a dual mixedvariational formulation for contact problem in elasticity is presented. The existence and uniqueness of the solution of the dual variationa...
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In this paper, based on the mixed variational formulation in [9], a dual mixedvariational formulation for contact problem in elasticity is presented. The existence and uniqueness of the solution of the dual variational problem are discussed,and the error bound O(he3/4) is obtained for Raviart-Thomas (k = 1) elementapproximation.
A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction ...
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A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.
In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m s...
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In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on M which is corresponding to the m step scheme defined on M while the old definitions are given out by defining a corresponding one step method on M × M ×…× M = Mm with a set of new variables. The new definition gives out a steptransition operator g: M → M. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator g will be constructed via continued fractions and rational approximations.
In the exact nonparametric illference, we frequelltly need the enumeration of all contingency tables with the same marginal totals. A qualltum jump toward a more rapid method took place with the publication of the net...
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In the exact nonparametric illference, we frequelltly need the enumeration of all contingency tables with the same marginal totals. A qualltum jump toward a more rapid method took place with the publication of the network approach of Mehta et al.[1-3]. It circumvents the need to explicitly enumerate each table and considerably extends the bounds of computational feasibility relative to the direct enumeration. In this paper) the present authors suggest another algorithm of implicit enumeration of all tables. First, a contingency table (T × c table or stratified 2×c table) is regarded as a number with several digits, and all contingency tables with the same marginal totals are regarded as a number sequence. A rule is then intyoduced to generate the sequence and to leap some subsequences which are useless for computing the probability values. The leaping subsequence aIgorithm proposed is more efficient than the network algorithm. Especially, when-the permutation distribution is required, our algorithm may run tens times faster than StatXact.[4]
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