応用数理

抄録を表示する抄録を非表示にする

This paper reviews the Kalman (or H_2) filter and the recent development of H_∞ filter, with a preliminary remark on earlier mathematical works related to the least-squares estimation. For the linear Gaussian state-space model, it is shown that the Kalman filter is a dynamical system that produces the least-squares estimates of the states given observations and that the Kalman gain is determined by the associated Riccati equation. We then show that the H_∞ filtering problem is a minimax estimation problem that minimizes the energy of estimation errors maximized over all possible disturbances and initial states. A comparison of the Kalman filter and the H_∞ filter is made in frequency domain to illustrate the basic feature of two filters. After a brief introduction of Krein space, we also show that the H_∞ (central) filter is the Kalman filter for a Krein space state-space model with indefinite noise Gramian.

抄録全体を表示

PDF形式でダウンロード (878K)

並列数値処理は,それが言われだしてから久しいにも関わらず,一般の科学技術計算ユーザには充分浸透して重宝がられている状態とはほど遠い.もちろんプログラミングの専門的技巧の極をつくして作られた一部の専門家集団の並列数値計算ソフトには成功したものもあるが,一般ユーザには,現在の並列計算機は汎用的に使いこなすにはプログラミングが繁雑でむつかしい.それでこのような状況のもとで,何が障害になっているか,またどのようなパターンの計算の場合,並列の加速を得ることができ,並列計算の恩恵を得ることに成功しているか,概観しようというのが本稿の目的である.

抄録全体を表示

After touching upon methods of acquiring data to be fitted, an outline of splines and their important algorithms are explained. Then, the problem of data fitting with a spline is formulated. From the viewpoint of obtaining fair or aesthetic curves, some historical descriptions on interpolation and approximation using splines are given. It is shown that location of good knots is an important issue in the data fitting using splines, and representative approaches for determining good knots are shown. Finally, a brief description of reverse engineering is given, and an effective example of data fitting in reverse engineering is introduced.

抄録全体を表示

J-STAGEへの登録はこちら（無料）