We consider a contour integral-based eigensolver that finds eigenvalues in a given domain and the corresponding eigenvectors of the generalized eigenvalue problem. In the contour integral-based eigensolver, quadrature points are placed in the complex plane in order to approximate the contour integral. When eigenvalues exist near a quadrature point, the accuracy of other eigenvalues is deteriorated. We herein propose a method by which to recover the accuracy of the eigenpairs when eigenvalues exist near a quadrature point. A numerical experiment is conducted in order to verify that the proposed method is efficient.

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The Cholesky QR algorithm is an ideal QR decomposition algorithm for high performance computing, but known to be unstable. We present error analysis of the Cholesky QR algorithm in an oblique inner product defined by a positive definite matrix, and show that by repeating the algorithm twice (called CholeskyQR2), its stability is greatly improved.

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In this paper, we discuss the optimal ate pairing over Barreto-Naehrig (BN) curves. First, we give an explicit formula for computing this pairing via elliptic nets associated to the twist curves. Second, we consider parallel algorithms to calculate elliptic nets for computing this pairing. Finally, we evaluate the costs of our parallel algorithms.

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The present paper describes a method finding bead shapes in shell structure to decrease the absolute value of mean compliance under periodic loading by using a solution to shape optimization method. Variation of the shell structure in out-of-plane direction is chosen as a design variable. To create beads, the out-of-plane variation is restricted by using the sigmoid function. The integrated absolute value of mean compliance in target frequency range is used as objective function. An iterative algorithm based on the $H^1$ gradient method is used to solve the problem. The effectiveness of the method is confirmed by numerical example.

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In this paper, an initial guess is proposed for Newton's method to compute the principal matrix square root, and a sufficient condition of the initial guess is shown for the quadratic convergence. Numerical examples indicate that the initial guess is promising for computing the principal square roots of overlap matrices arising from condensed matter physics.

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It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplications. We have already shown that they are also very effective for software-based multiple precision floating-point arithmetic environments such as the MPFR/GMP library. In this paper, we show that we can obtain the same effectiveness for double-double (DD) and quadruple-double (QD) environments supported by the QD library, and that parallelization can increase the speed of these multiple precision matrix multiplications. Finally, we demonstrate that our implemented parallelized Strassen and Winograd algorithms can increase the speed of parallelized LU decomposition.

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Improved Stabilized Approximate Inverse (ISAINV) based on A-orthogonalization process is known as an effective preconditioning technique for the conjugate gradient (CG) method to solve highly ill-conditioned linear systems. This research aims to accelerate the convergence of the finite element analysis of shell structures by preserving the sparsity in the preconditioning matrix and by parallelizing the localized process of ISAINV preconditioning. In the numerical results, the proposed ISAINV preconditioner shows better convergence and faster computational time than the conventional preconditioning.

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A truncation error of the interpolant is considered for a class of particle methods, which can describe Smoothed Particle Hydrodynamics (SPH). Owing to sufficient conditions of the weight function and a regularity of the family of discrete parameters, a truncation error estimate of the interpolant is established for a class of particle methods based on the Voronoi decomposition. Moreover, some numerical results are shown, which agree well with theoretical ones.

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We propose an optimization method for the boundary shape of a waveguide for a high-pass filter that passes electric signals. The waveguide is modeled as a boundary-value problem having the electromagnetic wave equation. The domain variation is chosen as a design variable, while the weighted power consumption on the input port is used as an objective function. Its shape derivative is derived theoretically using the adjoint variable method. To solve the shape-optimization problem, we use an iterative algorithm based on the $H^{1}$ gradient method. The numerical results obtained show the effectiveness of the proposed method.

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We introduce a credit portfolio risk model within the ``top-down approach'' and then demonstrate applicability of our model to practical credit risk management via some empirical studies using some historical data on down-grades of Japanese firms. Specifically we present a simple random thinning model with some latent factor so as to explain the fact that downgrades are observed in some sub-portfolio much more or much less than expected naively.

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A new solvable 3-dimensional spin lattice Hamiltonian with inhomogeneous couplings, which can be diagonalized by 3-variable Krawtchouk polynomials, is proposed. The model is defined on the lattice of rectangular pyramid and describes near-neighbor interactions instead of nearest-neighbor ones. Using the properties of 3-variable Krawtchouk polynomials, quantum state transfer in the model is analyzed. In particular, for some value of the parameters, perfect state transfer is shown to occur from the apex to the diagonal plane.

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A numerical model of a nonlinear and degenerate diffusion equation on connected graphs, arising in a diversity of industrial applications, is presented. This paper shows that concurrently using a staggered finite volume spatial discretization with an analytical solution-based flux evaluation method and an operator-splitting technique computes stable and physically-consistent numerical solutions to the equation. A demonstrative application example of the numerical model to moisture dynamics in a hypothetical non-woven fibrous strip network under an evaporative environment is presented in order to show its versatility. Mathematical issues to be addressed in a future for better comprehending the model are finally discussed.

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In the field of industrial shape design, the plane curves which have radii of curvature proportional to the power of linear functions of their arc-length parameters are called the log-aesthetic curves (LAC) and have been investigated. However, the well-used curves, for example, the parabolic arcs and the typical curves of Mineur et al. are not contained in the family of LACs. In this letter we generalize LAC by the Hamiltonian formalism. This extended family of curves contains some well-known plane curves in classical differential geometry.

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In this contribution, we propose a new framework to derive energy-preserving numerical schemes based on the variational principle for Hamiltonian mechanics. We focus on Noether's theorem, which shows that the symmetry with respect to time translation gives the energy conservation law. By reproducing the calculation of the proof of Noether's theorem after discretization using the summation by parts and the discrete gradient, we obtain the scheme and the corresponding discrete energy at the same time. The significant property of efficiency is that the appropriate choice of the discrete gradient makes our schemes explicit if the Hamiltonian is separable.

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This study provides a theoretical framework to understand how campaign advertising works in a referendum. Our model analyzes a referendum with a straight choice between two alternatives, Yes or No. In this model, after the parties decide their policies, they promise benefits to voters during the campaign, which ultimately results in a fiscal cost and, thus, a burden to the voters themselves. We construct a two-party two-stage game in which parties choose a policy in the first stage and the benefits in the second stage. We show that one party shifts to a more extreme (polarized) position in an equilibrium.

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The set of pairing-friendly elliptic curves that are generated by given polynomials forms a complete family. Although a complete family with a $\rho$-value of 1 is the ideal case, there is only one such example that is known. We prove that there are no ideal families with embedding degree 3, 4, or 6 and that many complete families with embedding degree 8 or 12 are nonideal, even if we choose noncyclotomic families.

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In recent years, many discrete variable methods using the exponential operator, called exponential integrator, have been presented, and various computational methods of the matrix exponential are also proposed. Especially the combination of the Padé approximant and the scaling and squaring method is most powerful and widely used. However, the squaring process is susceptible to roundoff errors. We propose a modified squaring process for the scaling and squaring methods. From the numerical results, an accuracy improvement about 1/100 is obtained in the best case.

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We give a brief report on our computations of linear determinantal representations of smooth plane cubics over finite fields. After recalling a classical interpretation of linear determinantal representations as rational points on the affine part of Jacobian varieties, we give an algorithm to obtain all linear determinantal representations up to equivalence. We also report our recent study on computations of linear determinantal representations of twisted Fermat cubics defined over the field of rational numbers.

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In this article, we discuss the mathematical analysis of neuronal firing in the brain based on the formulation by Sompolinsky (Sompolinsky, Proc. Natl. Acad. Sci., 1990). We first establish a Fokker-Planck equation corresponding to the original stochastic differential equation-based model, then discuss its well-posedness and global-in-time solvability. The asymptotic stability of the incoherence and some properties from the dynamical system aspect are also discussed.

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Recently, new spreading sequences have been proposed to increase the capacity of users. In particular, the Weyl spreading sequences have the larger capacity of users than the Gold codes. This paper shows that the Weyl spreading sequences appear in a bit recovering model and they are orthogonal basis vectors. This result shows the reason why they have the large capacity and that any spreading sequence is expressed as the sum of the Weyl spreading sequences.

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We consider conservative numerical methods for a certain class of PDEs, for which standard conservative methods are not effective. There, the standard skew-symmetric difference operators indispensable for the discrete conservation law cause undesirable spatial oscillations. In this letter, to circumvent this difficulty, we propose a novel ``average-difference method,'' which is tougher against such oscillations. However, due to the lack of the apparent skew-symmetry, the proof of the discrete conservation law becomes nontrivial. In order to illustrate partially the superiority, we compare the standard and proposed methods for the linear Klein--Gordon equation.

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