著者

鈴木 大慈

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.28, no.2, pp.28-33, 2018-06-26 (Released:2018-09-30)

参考文献数

16

被引用文献数

5

著者

長井 英生

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.13, no.4, pp.318-333, 2003-12-25 (Released:2017-04-08)

参考文献数

42

被引用文献数

2

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We give an overview of the studies of stochastic control and filtering theory, tracing the historical situation from Kalman-Bucy filtering, LQG stochastic control theory and their mathematical generalization to nonlinear systems and nonlinear filtering to H^∞ control and risk-sensitive stochastic control. Then we explain how we could formulate portfolio optimization problems for Merton's ICAPM, which are typical ones on mathematical finance, as risk-sensitive stochastic control problems based on understanding the situation, and analyze them by employing the methods established through such studies. Dynamic programming approach to stochastic control and the methods of measure change in nonlinear filtering apply to obtain explicit representation of optimal strategies for the portfolio optimization problems. More other aspects could be seen.

著者

佐藤 寛之 相原 研輔

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.28, no.4, pp.205-241, 2018 (Released:2018-12-26)

参考文献数

31

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概要. グラスマン多様体はシュティーフェル多様体の直交群による商多様体と見なすことができる.本論文では,そのような商多様体上の最適化問題を取り上げ,一般の目的関数に対して有効なニュートン法について議論する.特に,数値計算が行えるようにニュートン方程式を水平空間上の線形方程式として導出する.また,クリロフ部分空間法に基づき,目的関数のヘシアンの表現行列を陽に用いずに,方程式を効率よく求解する手法を提案する.

著者

池口 徹 合原 一幸

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.7, no.4, pp.260-270, 1997-12-15 (Released:2017-04-08)

参考文献数

25

被引用文献数

1

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This paper reviews such embedding theorems of dynamical systems as Takens' embedding theory and the extended theory by Sauer et al. and practical methods to reconstruct possible attractors only from observed time series data. These are bases for time series analysis from the view point of nonlinear dynamical systems theory. The reconstruction method by filtered delay coordinates is also discussed.

著者

池 祐一

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.32, no.3, pp.139-148, 2022-09-22 (Released:2022-12-26)

参考文献数

14

---

The recent applications of topological data analysis in machine learning are reviewed in this paper. Simplicial and persistent homology were briefly explained and then two such applications were described. The first application is a topological study of the activation of neural networks, and the second application is a convergence result for the stochastic subgradient method for topological loss functions.

著者

今井 功

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.3, no.4, pp.259, 1993-12-15 (Released:2017-04-08)

著者

梅野 健

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.32, no.1, pp.37-45, 2022-03-25 (Released:2022-06-30)

参考文献数

20

著者

石原 辰雄

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.12, no.3, pp.197-207, 2002-09-15 (Released:2017-04-08)

参考文献数

6

被引用文献数

1

---

In this paper, I derive expressions for the probability density function and the cumulative distribution function of a random variable composed of the sum and the product of n-independent uniform random variables distributed at different intervals. The numerical examples are shown to derive the probability density function in the case of three uniform random variables.

著者

立岡 文理 曽我部 知広 宮武 勇登 張 紹良

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.28, no.3, pp.142-161, 2018 (Released:2018-09-25)

参考文献数

11

---

概要. 本論文では数値積分による行列実数乗Aαの計算を考える.Aαの積分表示は減衰の遅い被積分関数の広義積分で表される.これまでは,変数変換により積分区間を有限にした後にGauss求積を用いて計算されてきたが,Aの条件数やαによっては収束性が悪化しうる.本論文では新たなアプローチとして二重指数関数型積分公式に着目し,積分区間の設定方法等をまとめたアルゴリズムを示したのち,その有用性を数値的に検証する.

著者

関口 英子

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.17, no.3, pp.256-258, 2007-09-26 (Released:2017-04-08)

著者

鷲尾 巧

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.20, no.1, pp.41-48, 2010-03-25 (Released:2017-04-08)

参考文献数

7

著者

上林 達

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.4, no.3, pp.211-228, 1994-09-15 (Released:2017-04-08)

参考文献数

13

---

This is an attempt to establish a framework of infinite dimensional information geometry. The space of the probability densikties on [0.1] which are absolutely continuous and the derivatives of which are square integrable is considered. The space is an open Hilbert manifold. The Fisher metric, however, is not compatible with the topology of the manifold. The unique existence of the covariant derivative which is metric and torsion free is proved, and the equation of the geodesic is shown. The equation is explicitly solved. It is proved that the manifold has some desirable geometrical characters.

著者

姫野 龍太郎

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.26, no.4, pp.38-42, 2017 (Released:2017-03-25)

参考文献数

8

著者

保國 惠一

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.28, no.2, pp.11-18, 2018 (Released:2018-09-30)

参考文献数

31

---

Linear systems involving singularity arise in a wide range of applications throughout computational science and engineering. This article aims at presenting and discussing iterative methods for solving linear systems with singularity, with an emphasis on stationary (matrix splitting) and Krylov subspace iterative methods and preconditioning techniques. For singular matrices, conventional preconditioners based on incomplete matrix factorizations may break down, whereas particular stationary iterative methods combined with Krylov subspace methods may avoid breakdown. Although classical stationary iterative methods have been regarded as slow to converge, recent stationary iterative methods have convergence speed competitive with Krylov subspace methods, and may dramatically improve the convergence of Krylov subspace methods when applied as preconditioners. We present recent results on their convergence theories in general and for particular problems such as saddle point systems and least squares problems.

著者

石井 雅治

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.17, no.1, pp.1-26, 2007-03-25 (Released:2017-04-08)

参考文献数

10

被引用文献数

1

---

In this paper, we set some assumptions for properties of neurons and study global structure of neurovarieties in a function space of 3-layered neural-networks by using these properties. Firstly we determine structure of regular points in neurovarieties as a submanifold of the function space by particularly using one of the properties "differentially strong non-degeneracy". Next we show a distribution of all singular points in the neurovarieties and internal structure of the singular points. Furthermore we show by using one of the properties "approximate degeneracy" that neurovarieties have folded structure.(Theory)

著者

山本 哲朗 菅野 幸夫

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.4, no.3, pp.251-258, 1994-09-15 (Released:2017-04-08)

参考文献数

14

---

The Durand-Kerner method is one of central techniques for finding all the zeros of a polynomial simultaneously. Interesting properties on this method have been obtained by several authors. In this paper, it is shown that some of them can be derived from the well known Lagrangian interpolation formula. Some remarks are also added.

著者

今野 浩

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.1, no.1, pp.36-50, 1991-03-15 (Released:2017-04-08)

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Recently, a remarkable progress has been made in the field of the global minimization of nonconvex functions over a polytope. The purpose of this article is to survey one of the most successful approaches in this field, namely parametric programming approaches to quasilinear nonconvex minimization problems. The problems to be discussed are: linear multiplicative programming problems, i. e., the minimization of the product of two affine functions; minimization of the sum of two linear fractional functions; minimization of concave quadratic functions and bilinear programming problems. It will be shown that a global minimum of a fairly large scale problems can be obtained efficiently by applying parametric simplex algorithms. Further, it will be shown that a convex multiplicative programming problems, i. e., the minimization of the product of two convex functions, can be solved by parametrizatioh and branch and bound techniques.

著者

鈴木 増雄

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:24240982)

巻号頁・発行日

vol.7, no.3, pp.257-264, 1997-09-15 (Released:2017-04-08)

参考文献数

7

---

The purpose of the present paper is to formulate the quantum analysis of multivariate operator functions f({A_j}) by introducing auxiliary operators {H_j} satisfying the conditions that [H_j, H_κ]=0 , [H_j, A_κ ]=0 for j≠κ, and [H_j, [H_κ, A_κ]]=0. Then we have d^nf=Σ_<j1>...<jn> δ_H_<J1>・・・δ_H_<jn>f using the inner derivation δ_A : δ_AQ=[A, Q]=AQ-QA. The operator Taylor expansion formula is given in the form : f({A_j+x_jdA_j})=e^Σ_j^x_j^d_jf({A_j})=exp(Σ_jx_jδ_H_j)f({A_j})=Σ_nΣ_<j1>...<jn>x_<j1>・・・x_<jn>δ<j1>..., _<jn>f≡Σ_nΣ_<j1>..., _<jn>x_<j1>・・・x_<jn>f^<(n)>_<j1>..., _<jn> : dA_<J1>・・・dA_jn with dA_j≡[H_j, A_j]=δ_H_jA_j, and with the partial derivatives {d_j} with respect to {A_j}. Here, δ_<j1>..., _<jn> denotes an ordered partial inner derivation, and n!f^<(n)>_<j1>...<jn> denotes the n th derivative of f({A_j}).

著者

石原 辰雄

出版者

一般社団法人 日本応用数理学会

雑誌

日本応用数理学会論文誌 (ISSN:09172246)

巻号頁・発行日

vol.12, no.3, pp.197-207, 2002

参考文献数

6

被引用文献数

1

---

In this paper, I derive expressions for the probability density function and the cumulative distribution function of a random variable composed of the sum and the product of n-independent uniform random variables distributed at different intervals. The numerical examples are shown to derive the probability density function in the case of three uniform random variables.

著者

萩原 学

出版者

一般社団法人 日本応用数理学会

雑誌

応用数理 (ISSN:24321982)

巻号頁・発行日

vol.26, no.1, pp.33-38, 2016 (Released:2016-07-27)

参考文献数

15