Japan Journal of Industrial and Applied Mathematics最新文献

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the generalized orthogonal matching pursuit (gOMP) algorithm. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is presented based on restricted isometry property (RIP) and restricted orthogonality constant (ROC).

In this paper, we consider a bidimensional renewal risk model with dependent main claims and delayed claims. Concretely, suppose that an insurance company simultaneously operates two kinds of businesses which separately trigger two types of claims named main claims and delayed claims, respectively, the two lines of businesses share a common claim-arrival counting process, and the random pairs from the two main claims as well as the random pairs from the two delayed claims, independent of each other, follow bivariate Farlie–Gumbel–Morgenstern distributions with different parameters. Assuming that all the claims are subexponential, an asymptotic formula of finite-time ruin probability for such a model is derived as the initial surpluses tend to infinity, which extends some recent ones in the literature.

In magnetic resonance imaging, high angular resolution diffusion imaging (abbr. HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient with higher order diffusion tensors from a diffusivity function. An intrinsic property of the diffusivity function is positive semi-definite, which reflects the phenomenon of water molecular diffusion in complicated biological tissue environments. In this paper, we provide a workable criterion for judging the positive semi-definiteness of a diffusivity function and shows that it is effective via two numerical examples.

This paper investigates mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds. In the first part, both necessary and sufficient optimality conditions for some types of efficient solutions are considered. After that, the Wolfe and Mond–Weir type dual problems are formulated and the duality relations under geodesic convexity assumptions are examined. Some examples are proposed to illustrate the results.

Abstract

In this paper, we study the structure of the least square solutions to overdetermined systems with no solution. In the main theorem, we prove that if an overdetermined system with no solution is deformed into a system of linear equations by the semi-equivalent deformations defined in this paper, then an approximate solution to the original overdetermined system with no solution can be given as the unique least square solution to the deformed system of linear equations. We also introduce some applications of our main theorem to practical inverse problems.

In a previous article, we have introduced a model to study life expectancy based on a sequence of Weibull distributions. Each of these distributions characterizes the living expectancy within a certain age interval. In the second step, we estimate the parameters for this model by combining the moment estimations and censoring methods. We have named this combination “the local parametric estimation method”. In this article, we present a different model that requires less number of random variable characteristics which help alleviate the estimation procedure. In fact, in comparison with the previous model, we are able to obtain an explicit formula for the variance of life expectancy. This is particularly useful in obtaining a normal approximation to life expectancy. Extensive computations with real-world datasets show that the local parametric method provides less biased estimation with lower variance in comparison to the Chiang method. This fact allows one to use statistical tests to detect life expectancy estimation differences as shown in the data where the Chiang method does not perform well. Additionally, the new life expectancy estimation method is also useful in the assessment of the health inequality in small area/small population settings by conducting statistical tests.

Abstract

Recently Oishi published a paper allowing lower bounds for the minimum singular value of coefficient matrices of linearized Galerkin equations, which in turn arise in the computation of periodic solutions of nonlinear delay differential equations with some smooth nonlinearity. The coefficient matrix of linearized Galerkin equations may be large, so the computation of a valid lower bound of the smallest singular value may be costly. Oishi’s method is based on the inverse of a small upper left principal submatrix, and subsequent computations use a Schur complement with small computational cost. In this note some assumptions are removed and the bounds improved. Furthermore a technique is derived to reduce the total computationally cost significantly allowing to treat infinite dimensional matrices.

The conjugate gradient (CG) method is the most basic iterative solver for large sparse symmetric positive definite linear systems. In finite precision arithmetic, the residual and error norms of the CG method often stagnate owing to rounding errors. The groupwise update is a strategy to reduce the residual gap (the difference between the recursively updated and true residuals) and improve the attainable accuracy of approximations. However, when there is a severe loss of information in updating approximations, it is difficult to sufficiently reduce the true residual and error norms. To overcome this problem, we propose a mixed-precision algorithm of the CG method using the groupwise update strategy. In particular, we perform the underlying CG iterations with the standard double-precision arithmetic and compute the groupwise update with high-precision arithmetic. This approach prevents a loss of information and efficiently avoids stagnation. Numerical experiments using double-double arithmetic demonstrate that the proposed algorithm significantly improves the accuracy of the approximate solutions with a small overhead of computation time. The presented approach can be used in other related solvers as well.

This paper develops a continuous approximation model for analyzing the effect of road pricing on the spatial distribution of traffic flow. The traffic flow density, which describes traffic flow as a function of position, is derived for a rectangular city with a grid network. The analytical expression for the traffic flow density demonstrates how the toll level, the size and shape of the toll area, and the shape of the city affect the spatial distribution of traffic flow. As the size of the toll area increases, reducing the traffic flow density at the city center becomes difficult. As the aspect ratio of the toll area increases, the traffic flow density at the city center increases. The shape of the city has less impact on the traffic flow density than the shape of the toll area.

This paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs.