The Bi-CGSTAB(L) proposed by Sleijpen, et.al. is one of iterative solvers for large and sparse nonsymmetric linear systems, and is used extensively. However, it is hard to estimate a suitable value of the restart number L for good convergence behavior in realistic problems. In this paper, we propose a way to select dynamically L for getting more efficient convergence behavior in Bi-CGSTAB(L). Finally, we compare the Bi-CGSTAB(L) using the dynamic selection of L with the original Bi-CGSTAB(L) by several numerical experiments.

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This paper is concerned with the maximum probability model and the mean-variance model, which arise in portfolio selection problems. We consider optimality conditions for the both problems and discuss a relationship between these two problems. By using the relation, we propose a method which solves effectively the maximum probability model. Specifically, we apply the Goldfarb-Idnani method to some kind of parametric quadratic programming problem for solving a nonlinear equation which follows from the relation. Some numerical experiments are given to show the performance of our method.

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Kantec method we propose is one of the simulation methods calculating air-flow rate at each air outlet of branch duct system. In this paper, we develop the discrete expressions based on energy equation with loss of energy, and demonstrate the effectiveness by comparison between the results obtained by our method and by our experiments.

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The Edwards-Wilkinson (EW) equation is a stochastic partial differential equation which mathematically models the growing rough surfaces. It has been pointed out that the variance of the solution of the EW equation diverges in spatial dimensions equal to or larger than 2. Based on mathematical and numerical analyses for the EW equation, we give two means to avoid the divergence. The first one is the smoothing of the EW equation by introducing a fourth order derivative. The second is to replace the Gaussian white noise with a less singularly correlated noise. These are confirmed by numerical calculations, and suggest a more reasonable modelling for the growing rough surface phenomenon.

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We propose a symbolic formulation for computing eigenvalues, eigenvectors and generalized eigenvectors of rational matrices. Based on the Frobenius normal forms of matrices, our formulation constructs the eigenvectors without solving a system of linear equations by Gaussian elimination over an algebraic extension field. The experimental results show that our algorithm is more efficient than a conventional method implemented on the existing computer algebra systems. Although both Reduce and Maple failed for middle-sized matrices because of the memory problem, our program succeeded in solving the eigenproblem for much larger matrices.

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