Japan Journal of Industrial and Applied Mathematics最新文献

Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, (hbox {L}^{natural })-convex sets, and (hbox {M}^{natural })-convex sets.

The main objective of this paper is to solve multi-linear systems with strong ( mathcal {M})-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.

As we know, the Jacobi–Davidson iteration method is very efficient for computing both extreme and interior eigenvalues of standard eigenvalue problems. However, the involved Jacobi–Davidson correction equation and the harmonic Rayleigh–Ritz process are more complicated and costly for computing the interior eigenvalues than those for computing the extreme eigenvalues. Thus, in this paper we adopt the originally elegant correction equation to generate the projection subspace in a skillful way, which is used to extract the desired eigenpair by the harmonic Rayleigh–Ritz process. The projection subspace, called as augmented Krylov subspace, inherits the benefits from both the standard Krylov subspace and the Jacobi–Davidson correction equation, which results in the constructed augmented Krylov subspace method being more effective than the Jacobi–Davidson method. A few numerical experiments are executed to exhibit the convergence and the competitiveness of the method.

This paper presents a new approach to selecting knots at the same time as estimating the B-spline regression model. Such simultaneous selection of knots and model is not trivial, but our strategy can make it possible by employing a nonconvex regularization on the least square method that is usually applied. More specifically, motivated by the constraint that directly designates (the upper bound of) the number of knots to be used, we present an (unconstrained) regularized least square reformulation, which is later shown to be equivalent to the motivating cardinality-constrained formulation. The obtained formulation is further modified so that we can employ a proximal gradient-type algorithm, known as GIST, for a class of nonconvex nonsmooth optimization problems. We show that under a mild technical assumption, the algorithm is shown to reach a local minimum of the problem. Since it is shown that any local minimum of the problem satisfies the cardinality constraint, the proposed algorithm can be used to obtain a spline regression model that depends only on a designated number of knots at most. Numerical experiments demonstrate how our approach performs on synthetic and real data sets.

In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel function. Iteration bounds for the large-update interior-point method and the small-update interior-point method are derived. It is shown that the large-update interior-point method has the same polynomial complexity as the small-update interior-point method, which is the best known iteration bounds. Our result closes a long-existing gap in the theoretical complexity bounds for large-update interior-point method and small-update interior-point method.

The forecasting of demand or cancellations is highly important for efficient revenue management in the hotel industry. Previous studies have mainly focused on the accuracy of the prediction of reservation number or cancellation rate on a specific accommodation or hotel chain; therefore, the application of the prediction to different accommodations or under the behavioral change of customers in response to natural or human events is difficult without the re-estimation of the prediction model. Information of the customer behavioral trend on the accommodation reservations is necessary for the construction of a general forecasting model. In this study, we focus on one of the general trends of customer behavior, that is, the reservation timing and the time changes of the cancellation probability using the big data of the reservation records provided by an online trip agency in Japan. We showed that the reservation timing and cancellation probability can be decomposed by five and six exponential functions of the days until the stay and the days from the reservations. We also showed that the significant factors influencing the time changing patterns are the guest numbers per room for both reservation and cancellation, composition of guests in terms of the number and gender of guests, and the stay length for reservation. These findings imply that the customer behavior during accommodation reservation could be categorized into multiple motivational factors toward reservations or cancellations. Our results contribute to the construction of a general forecasting model on the accommodation reservations.

The Sinc approximation applied to double-exponentially decaying functions is referred to as the DE-Sinc approximation. Because of its high efficiency, this method has been used in various applications. In the Sinc approximation, the mesh size and truncation numbers should be optimally selected to achieve its best performance. However, the standard selection formula has only been “near-optimally” selected because the optimal formula of the mesh size cannot be expressed in terms of elementary functions of truncation numbers. In this study, we propose two improved selection formulas. The first one is based on the concept by an earlier research that resulted in a better selection formula for the double-exponential formula. The formula performs slightly better than the standard one, but is still not optimal. As a second selection formula, we introduce a new parameter to propose truly optimal selection formula. We provide explicit error bounds for both selection formulas. Numerical comparisons show that the first formula gives a better error bound than the standard formula, and the second formula gives a much better error bound than the standard and first formulas.

We propose a linearizing-decoupling finite element method for the nonstationary diffusive Peterlin viscoelastic system with shear-dependent viscosity modeling the incompressible polymeric fluid flow, where the equation of the conformation tensor ({varvec{C}}) contains a diffusion term with a tiny diffusion coefficient (epsilon). By using the stabilizing terms (alpha _1^{-1} Delta ({varvec{u}}^{n+1} - {varvec{u}}^{n})) and (alpha _2^{-1} Delta ({varvec{C}}^{n+1} - {varvec{C}}^{n})), at every time level, the velocity ({varvec{u}}) and each component (C_{ij}) of the conformation tensor ({varvec{C}}) can be computed in parallel by our scheme. We obtain the error estimate (C(tau + h^2)) for the P2/P1/P2 element, where the constant C depends on the norm of the solution but is not explicitly related to the reciprocal of (epsilon). We conduct several numerical simulations and compute the experimental convergence rates to compare with the theoretical results.

This paper focuses on developing a numerical method with high-order accuracy for solving the time-dependent diffusion equation. We discrete time first, which results in a modified Helmholtz equation at each time level. Then, the quasi-compact difference method, which is derivative-free, is used to discretize the resulting Helmholtz equation. Theoretically, the stability and convergence analyses are performed by the aid of the Fourier method and error estimation, respectively. Numerically, Richardson extrapolation algorithm is utilized to improve the time accuracy, while the fast sine transformation is employed to reduce the complexity for solving the discretized linear system. Numerical examples are given to validate the accuracy and effectiveness of the proposed discretization method.