著者

Tomonori Kouya

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.8, pp.21-24, 2016 (Released:2016-05-13)

参考文献数

9

被引用文献数

5

---

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.

著者

Tomonori Kouya

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.6, pp.81-84, 2014 (Released:2014-12-17)

参考文献数

6

被引用文献数

2 5

---

The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as double-precision matrix multiplication by using these algorithms, no research to date has been undertaken to accelerate multiple precision matrix multiplication. In this paper, we propose a multiple precision matrix multiplication program for matrices of any size and test its performance. We also reveal special properties of our program through its application to LU decomposition.

著者

Yusuke Imoto Naoya Yamanaka Takeo Uramoto Masato Tanaka Masaki Fujikawa Naoto Mitsume

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.12, pp.29-32, 2020 (Released:2020-06-01)

参考文献数

7

被引用文献数

4

---

Hyper-dual numbers (HDN) are numbers defined by using nilpotent elements that differ from each other. The introduction of an operator to extend the domain of functions to HDN space based on Taylor expansion allows higher-order derivatives to be obtained from the coefficients. This study inductively defines matrix representations of HDN and proposes a numerical method for higher-order derivatives, called HDN-M differentiation, based on the matrix representations of HDN. The proposed method is characterized so that higher-order derivatives can be computed with matrix operation rules without implementations of the operation rules of HDN.

著者

Jirô Akahori Corina Constantinescu Kei Miyagi

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.12, pp.25-28, 2020 (Released:2020-05-24)

参考文献数

10

被引用文献数

2

---

In insurance mathematics, specifically in risk theory, mainly functional analytic techniques are used. In this paper, we give an alternative approach to deriving some well-known, basic, but important results on the classical collective risk model. Applying techniques based on Itô's calculus, we derive an integro-differential equation for the Gerber-Shiu function, under the Cramér-Lundberg model.

著者

Jeff Irion Naoki Saito

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.6, pp.21-24, 2014 (Released:2014-05-16)

参考文献数

16

被引用文献数

19

---

We describe a new transform that generates a dictionary of bases for handling data on a graph by combining recursive partitioning of the graph and the Laplacian eigenvectors of each subgraph. Similar to the wavelet packet and local cosine dictionaries for regularly sampled signals, this dictionary of bases on the graph allows one to select an orthonormal basis that is most suitable to one's task at hand using a best-basis type algorithm. We also describe a few related transforms including a version of the Haar wavelet transform on a graph, each of which may be useful in its own right.

著者

Hiroaki Seito Takeo Hoshi Yusaku Yamamoto

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.11, pp.13-16, 2019 (Released:2019-03-05)

参考文献数

11

---

We apply the shifted minimum residual method to a shifted linear system $(A+i\sigma I){\bf x}={\bf b}$ arising from quantum-mechanical wave packet simulation and discuss its advantages and disadvantages, comparing it with the widely used COCG method. Although the method requires more vector operations per iteration than the COCG method, it enjoys such nice properties as being free from breakdown, monotonic decrease of the residual norm and applicability to Hermitian-plus-shift systems, and can be a method of choice in some cases. Application of the method to the case of multiple shifts is also discussed.

著者

Atsushi Iwasaki Ken Umeno

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.9, pp.5-8, 2015 (Released:2017-02-18)

参考文献数

8

被引用文献数

2

---

Permutation polynomials over a ring of modulo $2^w$ are well adopted to digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator{s}. For a longer period of the polynomial is demanded in general, we derive a necessary and sufficient condition that polynomials are permutating and their periods are the longest over the ring. We call polynomials which satisfy the condition ``one-stroke polynomials over the ring''.

著者

Hiroaki Kuramae Takayasu Matsuo

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.4, pp.29-32, 2012 (Released:2012-10-26)

参考文献数

14

被引用文献数

8

---

A new procedure to design numerical schemes for coupled partial differential equations is proposed. The resulting schemes have discrete counterparts of conservative or dissipative quantity in original system. They also enjoy another welcome feature that they are constructed on staggered time meshes, by which each variables can be computed alternately with less computational costs than usual schemes. The procedure is demonstrated in the case of the coupled KdV equations.

著者

Yuki Tanaka Yutaka Yamaguti

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.15, pp.117-120, 2023 (Released:2023-11-16)

参考文献数

14

---

To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.

著者

Kazuhito Oguma Hideaki Ujino

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.1, pp.68-71, 2009 (Released:2009-12-23)

参考文献数

11

被引用文献数

2 2

---

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.

著者

Masaru Shintani Ken Umeno

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.14, pp.49-52, 2022 (Released:2022-04-06)

参考文献数

13

被引用文献数

1

---

We propose a new dynamic pricing algorithm based on the universal exponential law of booking curves in services with reservations. The algorithm includes a parametric learning model which makes it possible to simulate the effect of changes in prices on quantity demanded from historical data continuously for practical use. Furthermore, we show an example, where some real data in a hotel applies for the learning model. Our proposed algorithm with the learning model, which can dynamically update the optimum parameters, is envisaged to be utilized as a practical dynamic pricing strategy.

著者

Masaru Shintani Ken Umeno

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.14, pp.45-48, 2022 (Released:2022-04-06)

参考文献数

12

被引用文献数

2

---

The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

著者

Haruka Yamada Akira Imakura Tetsuya Sakurai

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.10, pp.61-64, 2018 (Released:2018-10-25)

参考文献数

8

---

Tensor renormalization group (TRG) is a coarse-graining algorithm for approximating the partition function using a tensor network in the field of elementary particle physics. Although the computational cost of TRG can be reduced using a randomized singular value decomposition, its computation time is still large. In this paper, we propose a cost-efficient cutoff method for calculating TRG by truncating small tensor elements. Numerical experiments showed that the proposed method is faster than the conventional one without degrading accuracy.

著者

Yukiko Kato

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.13, pp.60-63, 2021 (Released:2021-09-29)

参考文献数

15

被引用文献数

1

---

This study discusses the analysis method for obtaining solutions that allow de-escalation in international conflicts within the framework of the Graph Model for Conflict Resolution. CD games, a conflict type in which two decision-makers can choose Cooperate (C) or Defect (D) strategies, are analyzed by examining the state transition and stability of decision makers with a focus on reachability. Based on the analysis, a new conceptual set is proposed, called `de-escalation reachability,' which enables focused analysis on the conflict states while avoiding any influence of arbitrators' attributes.

著者

Yu Ichida Kaname Matsue Takashi Okuda Sakamoto

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.12, pp.65-68, 2020 (Released:2020-10-12)

参考文献数

10

被引用文献数

3

---

In this paper, we consider the asymptotic behavior of traveling wave solutions of a certain degenerate nonlinear parabolic equation for $\xi \equiv x - ct \to - \infty$ with $c>0$. We give a refined one of them, which was not obtained in the preceding work [Ichida-Sakamoto, J. Elliptic and Parabolic Equations, to appear], by an appropriate asymptotic study and properties of the Lambert $W$ function.

著者

Hiroyuki Sato

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.7, pp.13-16, 2015 (Released:2015-01-25)

参考文献数

8

被引用文献数

1 7

---

The joint singular value decomposition of multiple rectangular matrices is formulated as a Riemannian optimization problem on the product of two Stiefel manifolds. In this paper, the geometry of the objective function and the Riemannian manifold for this problem are studied to develop a Riemannian trust-region algorithm. The proposed algorithm globally and locally quadratically converges, and our numerical experiments demonstrate that it performs much better than the steepest descent method.

著者

Satoshi Hayakawa Ken'ichiro Tanaka

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.12, pp.21-24, 2020 (Released:2020-04-17)

参考文献数

8

被引用文献数

1

---

We give a mathematical analysis of potential-theoretical numerical integration formulas mainly proposed by Tanaka et al. over weighted Hardy spaces, which are spaces of analytic functions with a certain decay. We investigate the case of choosing sampling points by discrete energy minimization. In order to bound the convergence rate of the numerical integration error, we make use of the recent result of Hayakawa and Tanaka on the function approximation formula.

著者

Shunki Kyoya Ken'ichiro Tanaka

出版者

The Japan Society for Industrial and Applied Mathematics

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.11, pp.65-68, 2019 (Released:2019-09-23)

参考文献数

5

被引用文献数

1

---

The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation. However, it has a disadvantage that it is sensitive to singularities of an integrand near the real axis, and Slevinsky and Olver (SIAM J. Sci. Comput., 2015) attempted to improve it by constructing conformal maps based on the locations of singularities. In this letter, we construct a new transformation formula based on their ideas. This can be regarded as a generalization of the DE transformations. We confirm the effectiveness of this by a numerical experiment.

著者

Takashi Kato Akihiko Takahashi Toshihiro Yamada

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.5, pp.17-20, 2013 (Released:2013-03-06)

参考文献数

3

被引用文献数

2 7

---

This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our approximation method through numerical examples.

著者

Hiroya Hashimoto Takahiro Tsuchiya

出版者

一般社団法人 日本応用数理学会

雑誌

JSIAM Letters (ISSN:18830609)

巻号頁・発行日

vol.5, pp.13-16, 2013 (Released:2013-03-06)

参考文献数

6

被引用文献数

1

---

In this paper, we consider Euler-Maruyama approximations for 1-dimensional stochastic differential equations (SDEs) driven by rotation invariant (i.e. symmetric) $\alpha$ stable processes and discuss their rate of strong convergence by numerical simulations. We also study the relationship between the convergence rate and the index $\alpha$ of rotation invariant stable process and/or the exponent $\gamma$ of the Hölder continuity of the diffusion coefficient.