We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both models show phase transition from free flow to jam in a fundamental diagram. Moreover, the ultradiscrete model includes the Fukui--Ishibashi model in a special case.

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This paper concerns with the following linear programming problem: \[ \mbox{Maximize } c^tx, \mbox{ subject to } Ax \leqq b \mbox{ and } x\geqq 0, \] where $A \in \F^{m\times n}$, $b \in \F^m$ and $c, x \in \F^n$. Here, $\F$ is a set of floating point numbers. The aim of this paper is to propose a numerical method of including an optimum point of this linear programming problem provided that a good approximation of an optimum point is given. The proposed method is base on Kantorovich's theorem and the continuous Newton method. Kantorovich's theorem is used for proving the existence of a solution for complimentarity equation and the continuous Newton method is used to prove feasibility of that solution. Numerical examples show that a computational cost to include optimum point is about 4 times than that for getting an approximate optimum solution.

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In this paper we will construct compactly supported tight framelets with orientation selectivity and Gaussian derivative like filters. These features are similar to one of simple cells in V1 revealed by recent vision science. In order to see the orientation selectivity, we also give a simple example of image processing of a test image.

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We report our current effort on extracting morphological features from neuronal dendrite patterns using the eigenvalues of their graph Laplacians and clustering neurons using those features into different functional cell types. Our preliminary results indicate the potential usefulness of such eigenvalue-based features, which we hope to replace the morphological features extracted by methods that require extensive human interactions.

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In optimal shape problems the derivatives of costs with respect to shapes are important, because it gives a direction of lower cost from an initial shape. The differentiability of costs strongly depends on shape derivatives of solutions of mechanical problems, stationary linearized flow problems, the Stokes problems. The shape derivatives are usually given automatically by the associated material derivatives. We show the convergence of shape difference quotients under sufficient conditions. These conditions are applied to the existence of the shape derivatives of the velocity and the pressure in the Stokes problems.

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In this paper, we consider a numerical verification method of solutions for nonlinear elliptic boundary value problems with very high accuracy. We derive a constructive error estimates for the $H^1_0$-projection into polynomial spaces by using the property of the Legendre polynomials. On the other hand, the Galerkin approximation with higher degree polynomials enables us to get very small residual errors. Combining these results with existing verification procedures, several verification examples which confirm us the actual effectiveness of the method are presented.

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Exact solutions of the ultradiscrete Sine-Gordon equation which have oscillating structure are constructed. They are considered to be a counterpart of the breather solution of the Sine-Gordon equation. They are given by setting specific parameters in the discrete soliton solutions and ultradiscretizing the resulting solutions.

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We provide a formal model for protocols using ring signatures and prove that this model is computationally sound: if there is an attack in the computational world, then there is an attack in the formal (abstract) model. Our original contribution is that we consider security properties, such as anonymity, which are not properties of a single execution trace, while considering an unbounded number of sessions of the protocol.

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The Anderson method provides a significant acceleration of convergence in solving nonlinear simultaneous equations by trying to minimize the residual norm in a least-square sense at each iteration step. In the present study I use singular value decomposition to reformulate the Anderson method. The proposed version contains only a single parameter which should be determined in a trial-and-error way, whereas the original one contains two. This reduction leads to stable convergence in real-world self-consistent electronic structure calculations.

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The discrete hungry Lotka-Volterra (dhLV) system is already shown to be applied to matrix eigenvalue algorithm. In this paper, we discuss a form of the dhLV system named as the qd-type dhLV system and associate it with a matrix eigenvalue computation. Along a way similar to the dqd algorithm, we also design a new algorithm without cancellation in terms of the qd-type dhLV system.

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In this paper, we design new algorithms for eigendecomposition. With the help of the Newton iterative method, we solve a nonlinear quadratic system whose solution is equal to an eigenvector on a hyperplane. By choosing normal vector of the hyperplane in the orthogonal complement of the space spanned by already obtained eigenvectors, all eigenpairs are sequentially obtained by solving the quadratic systems.

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In this paper, the influence of errors which arise in matrix multiplications on the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed. In order to generate high accuracy solutions, a new Block Krylov subspace method named “Block BiCGGR” is also proposed. Some numerical experiments illustrate that the Block BiCGGR method can generate high accuracy solutions compared with the Block BiCGSTAB method.

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The I-SVD algorithm is a singular value decomposition algorithm consisting of the mdLVs scheme and the dLV twisted factorization. By assigning each piece of computations to each core of a multi-core processor, the I-SVD algorithm is parallelized partly. The basic idea is a use of splitting and deflation in the mdLVs. The splitting divides a bidiagonal matrix into two smaller matrices. The deflation gives one of the singular values, and then the corresponding singular vector becomes computable by the dLV. Numerical experiments are done on a multi-core processor, and the algorithm can be about 5 times faster with 8 cores.

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A contour integral method is proposed to solve nonlinear eigenvalue problems numerically. The target equation is $F(\lambda)\bm{x}=0$, where the matrix $F(\lambda)$ is an analytic matrix function of $\lambda$. The method can extract only the eigenvalues $\lambda$ in a domain defined by the integral path, by reducing the original problem to a linear eigenvalue problem that has identical eigenvalues in the domain. Theoretical aspects of the method are discussed, and we illustrate how to apply of the method with some numerical examples.

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We analyze convergence properties and numerical properties of the differential qd algorithm generalized for totally nonnegative band matrices. In particular, we show that the algorithm is globally convergent and can compute all eigenvalues to high relative accuracy.

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To make clear geometrical structure of an arbitrarily given pencil, it is crucial to understand Kronecker structure of the pencil. For this purpose, GUPTRI is the only practical numerical algorithm at present. However, although GUPTRI determines the Kronecker canonical form (KCF), it does not give any direct information on Kronecker bases (KB). In this paper, we propose a numerical algorithm which gives a full of information on Kronecker structure including KB as well as KCF. The main ingredient of the algorithm is singular value decompositions, which guarantee the backward stability of the algorithm.

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This paper studies the robust exponential hedging in a Brownian factor model, giving a solvable example using a PDE argument. The dual problem is reduced to a standard stochastic control problem, of which the HJB equation admits a classical solution. The optimal strategy will be expressed in terms of the solution to the HJB equation.

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Through an extension of an ultradiscrete optimal velocity (OV) model, we introduce an ultradiscretizable traffic flow model, which is a hybrid of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a generalization of a special case of the ultradiscrete OV (uOV) model recently proposed by Takahashi and Matsukidaira. A phase transition from free to jam phases as well as the existence of multiple metastable states are observed in numerically obtained fundamental diagrams for cellular automata (CA), which are special cases of the ultradiscrete limit of the hybrid model.

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In this paper, we have proposed a new compressible fluid model for the one-dimensional traffic flow taking into account a variation of the reaction time of drivers, which is based on the actual measurements. The model is a generalization of the Payne model by introducing a density-dependent function of reaction time. The linear stability analysis of this new model shows the instability of homogeneous flow around a critical density of vehicles, which is observed in real traffic flow. Moreover, the condition of the nonlinear saturation of density against small perturbation is theoretically derived from the reduction perturbation method.

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In this paper, we present perturbation results for eigenvalues of a matrix pencil of Hankel matrices for which the elements are given by complex moments. These results are extended to the case that matrices have a block Hankel structure. The influence of quadrature error on eigenvalues that lie inside a given integral path can be reduced by using Hankel matrices of an appropriate size. These results are useful for discussing the numerical behavior of root finding methods and eigenvalue solvers which make use of contour integrals. Results from some numerical experiments are consistent with the theoretical results.

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