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.
Some numerical tests are finished in this paper for raising the ability to find solutions of Denton-scheme. First, three improvement opinions of concrete algorithm for Denton-Scheme are presented. Then, the computatio...
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Some numerical tests are finished in this paper for raising the ability to find solutions of Denton-scheme. First, three improvement opinions of concrete algorithm for Denton-Scheme are presented. Then, the computational accuracy of numerical solutions is checked with three typical examples, also a quantitative estimation for computational accuracy is described. Finally, the maximum flux of mass through plane cascades is determined by numerical tests. A lot of tests shows that the ability to find solutions of this program is fairly raised with algorithm improvements of this paper.
In this paper, two nonconforming finite elements are discussed. They pass the generlized patch test and can be used in the numerical solution of second order elliptic problems.
In this paper, two nonconforming finite elements are discussed. They pass the generlized patch test and can be used in the numerical solution of second order elliptic problems.
In the present paper, the authors suggest an algorithm to evaluate the multivariate normal integrals under the supposition that the correlation matrix R is quasi-decomposable, in which we have rij = aiaj for most i, j...
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In the present paper, the authors suggest an algorithm to evaluate the multivariate normal integrals under the supposition that the correlation matrix R is quasi-decomposable, in which we have rij = aiaj for most i, j, and rij = aiaj + bij for the others, where bij’s are the nonzero deviations. The algorithm makes the high-dimensional normal distribution reduce to a 2-dimensional or 3-dimensional integral which can be evaluated by the numerical method with a high *** supposition is close to what we encounter in practice. When correlation matrix is arbitrary, we suggest an approximate algorithm with a medium precision, it is, in general, better than some approximate algorithms. The simulation results of about 20000 high-dimensional integrals showed that the present algorithms were very efficient.
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