Japan Journal of Industrial and Applied Mathematics最新文献

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.

In this paper, inspired by the simplified relaxed alternating positive semi-definite splitting preconditioner (Xiong and Li in J Appl Math Comput, 2023), a modified preconditioner is established to solve the three-by-three block saddle point problems. The advantage of the modified preconditioner is that its parameters can be easy to select, which can avoid the work of the calculation of the parameters. Next, the spectral property of the preconditioned matrix with modified preconditioner is also discussed. In the end, three examples are provided to show the effectiveness of the modified preconditioner.

Variable preconditioning methods for Krylov-type linear equation solvers have become popular thanks to their faster convergence speed compared to conventional methods, such as, the Incomplete Lower-Upper factorization and point Jacobi methods. Recently, Kushida and Okuda have introduced a variable preconditioning method, which updates the preconditioning matrix using the Broyden–Fletcher–Goldfarb–Shanno scheme, and applied it to the generalized minimum residual recursive scheme (GMRESR), which is a variant of the well-known GMRES method. Although their method indicated a superior performance to the conventional methods, the problems employed in their study were academic, and its performance on practical problems is of interest. In this study, we evaluate the feasibility of their variable preconditioning for practical problems. FrontISTR, which is a well established open-source parallel finite element analysis program and well used in the industrial field, is employed as the framework to implement the above-mentioned Kushida and Okuda’s preconditioning method in GMRESR (Self-Updating Preconditioning GMRESR; SUP-GMRESR). As results, (1) SUP-GMRESR indicated approximately a three-fold faster convergence than GMRES, which is one of the default linear equation solvers implemented on FrontISTR, using a 600 million degrees of freedom problem, and (2) SUP-GMRESR converged even when GMRES suffered from a stagnation.