Japan Journal of Industrial and Applied Mathematics最新文献

The fixed point iteration method is an effective method for solving absolute value equation via equivalent two-by-two block form. To further improve the computational efficiency of the fixed point iteration method, by using the preconditioned shift-splitting strategy, we propose an inexact fixed point iteration method for solving absolute value equation in this paper. We obtain some convergence conditions for the proposed method. The effectiveness of the proposed method are shown by three examples.

Optical fibers are among the most widely used tools in information communication today, and they have had an active development trajectory. Film interconnection is among the methods applied to optical fibers. However, due to its characteristics, the interconnection design must be done well so that each fiber satisfies several design requirements. In this study, we developed a mathematical model for automatic wiring design using film optical fiber interconnections. To design optical fiber routing from the top to the bottom of the film, we propose an exact solution method using a mixed-integer programming problem and a heuristic method based on the exact solution method. In this paper, we compare the results of our methods with rule-based methods and confirm that our methods are superior. For the experiments, we created sample data based on a previous joint research project with Sumitomo Electric Industries, Ltd. and used it. Additionally, we investigated conditions for wiring design, and this paper discusses conditions for obtaining more efficient wiring methods.

We discuss how to compute the Brauer group of the product of two elliptic curves over a finite field. Specifically, we apply the Artin–Tate formula for abelian surfaces to give a simple formula for computing the order of the Brauer group of the product of two elliptic curves. Our formula enables to compute the order of the Brauer group using traces of Frobenius maps on elliptic curves and the discriminant of the group of homomorphisms between two elliptic curves. In addition, for the product of non-isogenous elliptic curves, we give an algorithm for computing torsion subgroups of a certain Galois cohomology that can be embedded as subgroups of the Brauer group.

In this paper, a new stochastic volatility model for pricing European call option is proposed, which introduces the regime-switching mechanism controlled by Markov chain in stochastic volatility and stochastic long-term mean. The advantage of adopting this new model is that it can deduce a colsed-form solution of European call option based on characteristic function of the underlying price, which can save a lot of time and effort when applied in the real market. The effect of introducing regime-switching into European call option pricing model is investigated through numerical experiments, and the results show that the regime-switching has a significant effect on the model. The empirical results further demonstrate that our model has some advantages over the other two models.

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.